Costs and estimated earnings in excess of billings on uncompleted contracts Contract with Customer, Asset, after Allowance for Credit Loss, Current Property, Plant and Equipment [Table] Property, Plant and Equipment [Table] Cover [Abstract] Cover [Abstract] Fixed-price contracts Fixed-Price Contract [Member] Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect, Total Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect Operating lease right-of-use assets Operating Lease, Right-of-Use Asset Asset backed credit facility, fixed charged coverage ratio requirement, maximum Asset Backed Credit Facility Fixed Charge Coverage Ratio Requirement, Maximum Asset Backed Credit Facility Fixed Charge Coverage Ratio Requirement, Maximum Other accrued expenses Other Liabilities, Current Business Segments [Axis] Segments [Axis] Trading Symbol Trading Symbol Segment Reporting Information [Line Items] Segment Reporting Information [Line Items] Property, Plant and Equipment [Abstract] Computation of Basic and Diluted Earnings Per Share Schedule of Earnings Per Share, Basic and Diluted [Table Text Block] Earnings per Common Share Earnings Per Share [Text Block] Treasury shares sold to Employee Stock Purchase Plan Treasury shares sold to Employee Stock Purchase Plan Stock Issued During Period, Value, Employee Stock Purchase Plan Income taxes Income Taxes Paid, Net Crude Oil Terminal Project Crude Oil Terminal Project [Member] Crude Oil Terminal Project Stockholders’ equity: Equity, Attributable to Parent [Abstract] Segments [Domain] Segments [Domain] Accounts receivable, net of allowance for credit losses Increase (Decrease) in Accounts Receivable Basis of Presentation and Significant Accounting Policies Basis of Presentation and Significant Accounting Policies [Text Block] Loss Contingency Actions Taken By Defendant, Minimum Loss Contingency Actions Taken By Defendant, Minimum Loss Contingency Actions Taken By Defendant, Minimum Income Tax Disclosure [Abstract] Income Tax Disclosure [Abstract] Common stock, shares, outstanding (in shares) Common Stock, Shares, Outstanding Other Other Nonoperating Income (Expense) Statement of Stockholders' Equity [Abstract] Statement of Stockholders' Equity [Abstract] Other intangible assets, net of accumulated amortization Intangible Assets, Net (Excluding Goodwill) Operating lease liabilities Operating Lease, Liability, Noncurrent Long-Lived Tangible Asset [Axis] Long-Lived Tangible Asset [Axis] Revenue from Contract with Customer [Abstract] Revenue from Contract with Customer [Abstract] Billings on uncompleted contracts in excess of costs and estimated earnings Billings on uncompleted contracts in excess of costs and estimated earnings Contract with Customer, Liability, Current United States UNITED STATES Other assets, non-current (Note 2) Other Assets, Noncurrent Entity Tax Identification Number Entity Tax Identification Number Unused credit facility fee, percentage Line of Credit Facility, Unused Capacity, Commitment Fee Percentage Treasury Stock, Shares, Acquired Treasury Stock, Shares, Acquired Other income (expense): Other Nonoperating Income (Expense) [Abstract] Net contract liabilities Contract with customer, current liability, net Contract with customer, current liability, net Net Cash Provided by (Used in) Operating Activities, Total Net Cash Provided by (Used in) Operating Activities Treasury Stock, Common Treasury Stock, Common [Member] Operating activities: Net Cash Provided by (Used in) Operating Activities [Abstract] Intersegment Eliminations Intersegment Eliminations [Member] Project [Domain] Project [Domain] Prepaid expenses and other current assets Prepaid Expense, Current Equity Components [Axis] Equity Components [Axis] Local Phone Number Local Phone Number Process and Industrial Facilities [Member] Process and Industrial Facilities [Member] Process and Industrial Facilities Entity Common Stock, Shares Outstanding Entity Common Stock, Shares Outstanding Deferred income taxes Deferred Income Tax Liabilities, Net Other assets and liabilities Increase (Decrease) in Other Operating Assets Changes in operating assets and liabilities increasing (decreasing) cash: Increase (Decrease) in Operating Capital [Abstract] Diluted EPS: Earnings Per Share, Diluted [Abstract] Loss Contingency, Actions Taken by Defendant Loss Contingency, Actions Taken by Defendant Non-cash investing and financing activities: Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract] Entity Small Business Entity Small Business Geographical [Axis] Geographical [Axis] Long-Lived Tangible Asset [Domain] Long-Lived Tangible Asset [Domain] Asset backed line of credit, balance limit for fixed charge, coverage ratio mtrx:AssetBackedLineofCreditBalanceLimitforFixedChargeCoverageRatio mtrx:AssetBackedLineofCreditBalanceLimitforFixedChargeCoverageRatio Commitments and Contingencies Commitments and Contingencies Disclosure [Text Block] Debt Disclosure [Abstract] Debt Disclosure [Abstract] Restricted Stock, Value, Shares Issued Net of Tax Withholdings Restricted Stock, Value, Shares Issued Net of Tax Withholdings Common Stock Common Stock [Member] Treasury shares sold to Employee Stock Purchase Plan (in shares) Stock Issued During Period, Shares, Employee Stock Purchase Plans Nonvested restricted stock shares (in shares) Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount Additional margin on adjusted term SOFR, maximum Additional Margin On Adjusted Term SOFR Maximum Additional Margin On Adjusted Term SOFR Maximum Entity Emerging Growth Company Entity Emerging Growth Company Compensating balance Compensating Balance, Amount Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Beginning of Period Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, End of Period Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents Segment Reporting [Abstract] Segment Reporting [Abstract] Entity Central Index Key Entity Central Index Key Current assets: Assets, Current [Abstract] Goodwill Goodwill Consolidation Items [Axis] Consolidation Items [Axis] Other comprehensive income (loss), net of tax: Other Comprehensive Income (Loss), Net of Tax [Abstract] Corporate Segment Corporate Segment [Member] Treasury stock, common, shares (in shares) Treasury Stock, Common, Shares Equity Component [Domain] Equity Component [Domain] Loss Contingency ActionsTaken By Defendant, Maximum Loss Contingency ActionsTaken By Defendant, Maximum Segment Information Segment Reporting Disclosure [Text Block] Repurchase of common stock for payment of statutory taxes due on equity-based compensation Payments for Repurchase of Other Equity Adjustments to reconcile net loss to net cash provided (used) by operating activities: Adjustments, Noncash Items, to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract] Stock-based compensation expense APIC, Share-Based Payment Arrangement, Increase for Cost Recognition Asset backed credit facility, federal funds rate addition Asset Backed Credit Facility, Federal Funds Rate Addition Asset Backed Credit Facility, Federal Funds Rate Addition Entity Shell Company Entity Shell Company Comprehensive loss Comprehensive Income (Loss), Net of Tax, Attributable to Parent Entity Incorporation, State or Country Code Entity Incorporation, State or Country Code Asset backed credit facility, adjusted term SOFR one-month tenor, basis points Asset Backed Credit Facility Adjusted Term SOFR One Month Add On Asset Backed Credit Facility Adjusted Term SOFR One Month Add On Statement of Other Comprehensive Income [Abstract] Security Exchange Name Security Exchange Name Statement [Table] Statement [Table] Additional margin on alternate base rate loans, maximum Line Of Credit Basis Spread On Alternate Base Rate Maximum Line of credit basis spread on alternate base rate maximum. Basic EPS: Earnings Per Share, Basic [Abstract] Change in net contract balances Change in net contract balances Change in net contract balances from the prior year to the current year. Consolidation Items [Domain] Consolidation Items [Domain] Asset backed credit facility, adjusted term SOFR rate, minimum Asset Backed Credit Facility Adjusted Term SOFR Rate Minimum Asset Backed Credit Facility Adjusted Term SOFR Rate Minimum City Area Code City Area Code Current liabilities: Liabilities, Current [Abstract] Property, plant and equipment, net Property, Plant and Equipment, Net Total liabilities Liabilities Interest Interest Paid, Excluding Capitalized Interest, Operating Activities Storage and Terminal Solutions [Member] Storage and Terminal Solutions [Member] Storage and Terminal Solutions Foreign currency translation gain (loss) Other comprehensive income (loss) Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax Common stock, par value (in dollars per share) Common Stock, Par or Stated Value Per Share Total current assets Assets, Current Statement of Cash Flows [Abstract] Statement of Cash Flows [Abstract] Investing activities: Net Cash Provided by (Used in) Investing Activities [Abstract] Accrued expenses Increase (Decrease) in Accrued Liabilities Line of credit facility, remaining borrowing capacity Line of Credit Facility, Remaining Borrowing Capacity Performance obligations to be recognized as revenue within next twelve months Performance obligations to be recognized as revenue within next twelve months Performance obligations to be recognized as revenue within next twelve months. Operating lease liabilities Operating Lease, Liability, Current Common stock, shares issued (in shares) Common Stock, Shares, Issued Schedule of Segment Reporting Information, by Segment [Table] Schedule of Segment Reporting Information, by Segment [Table] Line of credit facility, maximum borrowing capacity Line of Credit Facility, Maximum Borrowing Capacity Statement Condensed Consolidated Balance Sheets [Abstract] Statement Condensed Consolidated Balance Sheets [Abstract] Statement Condensed Consolidated Balance Sheets [Abstract] Subsequent Event Type [Axis] Subsequent Event Type [Axis] Income Taxes Income Tax Disclosure [Text Block] Earnings Per Share [Abstract] Earnings Per Share [Abstract] Retained earnings Retained Earnings (Accumulated Deficit) Inventories Increase (Decrease) in Inventories Common stock, shares authorized (in shares) Common Stock, Shares Authorized Organization, Consolidation and Presentation of Financial Statements [Abstract] Organization, Consolidation and Presentation of Financial Statements [Abstract] Basis of Presentation Basis of Accounting, Policy [Policy Text Block] Weighted Average Number of Shares Outstanding Diluted Diluted weighted average shares outstanding (in shares) Weighted Average Number of Shares Outstanding, Diluted Net Cash Provided by (Used in) Financing Activities, Total Net Cash Provided by (Used in) Financing Activities Contract with Customer, Basis of Pricing [Axis] Contract with Customer, Basis of Pricing [Axis] Change in CIE Change in CIE Change in CIE from prior year to the current period. Treasury stock, at cost — 338,015 and 579,422 shares as of September 30, 2024 and June 30, 2024, respectively; Treasury Stock, Value Amendment Flag Amendment Flag Entity Registrant Name Entity Registrant Name Loss (gain) on disposal of property, plant and equipment (Note 3) Gain on disposition of assets Gain (Loss) on Disposition of Property Plant Equipment Retentions to be collected within one year Construction Contractor, Receivable, Retainage, Year One Accumulated other comprehensive loss Accumulated Other Comprehensive Income (Loss), Foreign Currency Translation Adjustment, Net of Tax Depreciation and amortization Depreciation, Depletion and Amortization Gross profit Gross Profit Gross Profit Property, Plant and Equipment Property, Plant and Equipment Disclosure [Text Block] Letters of credit outstanding, amount Letters of Credit Outstanding, Amount Selling, general and administrative expenses Selling, General and Administrative Expense Asset backed credit facility, fixed charge coverage ratio requirement, minimum Asset Backed Credit Facility Fixed Charge Coverage Ratio Requirement, Minimum Asset Backed Credit Facility Fixed Charge Coverage Ratio Requirement, Minimum Debt Debt Disclosure [Text Block] Geographical [Domain] Geographical [Domain] Accounts receivable, net of allowance for credit losses Accounts Receivable, after Allowance for Credit Loss, Current Contracts receivable, claims and uncertain amounts Contracts Receivable, Claims and Uncertain Amounts Summary of Revenue by Contract Type Disaggregation of Revenue [Table Text Block] Entity Address, Postal Zip Code Entity Address, Postal Zip Code Document Fiscal Period Focus Document Fiscal Period Focus Title of 12(b) Security Title of 12(b) Security Common stock — $0.01 par value; 60,000,000 shares authorized; 27,888,217 shares issued at September 30, 2024 and June 30, 2024, respectively; 27,550,202 and 27,308,795 shares outstanding as of September 30, 2024 and June 30, 2024, respectively; Common Stock, Value, Issued Assets Assets [Abstract] Mining and Minerals Project Mining and Minerals Project [Member] Mining and Minerals Project Document Type Document Type Utility and Power Infrastructure [Member] Utility and Power Infrastructure [Member] Utility and Power Infrastructure. Treasury shares purchased to satisfy tax withholding obligations Other Treasury Share Purchases Other treasury share purchases. Cash and cash equivalents Cash and Cash Equivalents, at Carrying Value Effect of exchange rate changes on cash Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Including Disposal Group and Discontinued Operations Net Cash Provided by (Used in) Financing Activities [Abstract] Net Cash Provided by (Used in) Financing Activities [Abstract] Summary of Contract with Customer, Contract Asset, Contract Liability, and Receivable Contract with Customer, Contract Asset, Contract Liability, and Receivable [Table Text Block] Project [Axis] Project [Axis] Basic loss per common share (in dollars per share) Basic loss per share (in dollars per share) Earnings Per Share, Basic Accounts payable Increase (Decrease) in Accounts Payable Accounts payable Accounts Payable, Current Proceeds from issuance of common stock under employee stock purchase plan Proceeds from Stock Plans Current Fiscal Year End Date Current Fiscal Year End Date Purchases of property, plant and equipment on account Capital Expenditures Incurred but Not yet Paid Loss before income tax expense Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest Total current liabilities Liabilities, Current Total assets Segment assets Assets Disaggregation of Revenue [Line Items] Disaggregation of Revenue [Line Items] Cost of revenue Cost of Goods and Services Sold Antidilutive Securities Excluded from the Calculation of Diluted EPS Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block] Income taxes receivable Income Taxes Receivable, Current Capital expenditures Payments to Acquire Property, Plant, and Equipment Other liabilities, non-current Other Liabilities, Noncurrent Commitments and contingencies (Note 6) Commitments and Contingencies Additional Paid-in Capital Additional Paid-in Capital [Member] Costs and estimated earnings in excess of billings on uncompleted contracts Increase (Decrease) in Contract with Customer, Asset Subsequent Event Type [Domain] Subsequent Event Type [Domain] Asset backed line of credit, percentage limit for fixed charge, coverage ratio mtrx:AssetBackedLineofCreditPercentageLimitforFixedChargeCoverageRatio mtrx:AssetBackedLineofCreditPercentageLimitforFixedChargeCoverageRatio Restricted cash Restricted Cash, Noncurrent Revenue Revenues Accounting Standards Not Yet Adopted New Accounting Pronouncements, Policy [Policy Text Block] Accrued insurance Accrued Insurance, Current Diluted loss per common share (in dollars per share) Diluted loss per share (in dollars per share) Earnings Per Share, Diluted Entity Interactive Data Current Entity Interactive Data Current Summary of Revenue by Geographic Areas Revenue from External Customers by Geographic Areas [Table Text Block] Billings on uncompleted contracts in excess of costs and estimated earnings Increase (Decrease) in Contract with Customer, Liability Entity Address, City or Town Entity Address, City or Town Canada CANADA Net loss Net income (loss) Net Income (Loss) Attributable to Parent Total Revenue Revenue from Contract with Customer, Including Assessed Tax Disaggregation of Revenue [Table] Disaggregation of Revenue [Table] Statement of Financial Position [Abstract] Statement of Financial Position [Abstract] Loss Contingencies [Table] Loss Contingencies [Table] Additional margin on adjusted term SOFR, minimum Additional Margin On Adjusted Term SOFR Minimum Additional Margin On Adjusted Term SOFR Minimum Line of credit facility, borrowing base Line of Credit Facility, Current Borrowing Capacity Stock-based compensation expense Share-Based Payment Arrangement, Noncash Expense Alternate base rate margin Alternate Base Rate Margin Alternate Base Rate Margin Net loss Net Income (Loss), Including Portion Attributable to Noncontrolling Interest Entity File Number Entity File Number Provision for federal, state and foreign income taxes Income Tax Expense (Benefit) Revenue Revenue from Contract with Customer [Text Block] Restricted Stock, Shares Issued Net of Shares for Tax Withholdings Restricted Stock, Shares Issued Net of Shares for Tax Withholdings Document Fiscal Year Focus Document Fiscal Year Focus Income Statement [Abstract] Income Statement [Abstract] Entity Address, Address Line One Entity Address, Address Line One Supplemental disclosure of cash flow information: Supplemental Cash Flow Information [Abstract] Document Period End Date Document Period End Date Contract with Customer, Basis of Pricing [Domain] Contract with Customer, Basis of Pricing [Domain] Contract retentions collectible beyond one year Construction Contractor, Receivable, Retainage, after Year One Other international Other international [Member] Other international [Member] Other Other Noncash Income (Expense) Effective Income Tax Rate Reconciliation, Percent Effective Income Tax Rate Reconciliation, Percent Net Cash Provided by (Used in) Investing Activities, Total Net Cash Provided by (Used in) Investing Activities Operating loss Operating Income (Loss) Operating Income (Loss) Interest expense Interest Expense, Operating and Nonoperating Valuation allowances placed on deferred tax assets Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Amount Total liabilities and stockholders’ equity Liabilities and Equity Accrued wages and benefits Employee-related Liabilities, Current Additional paid-in capital Additional Paid in Capital Cost of Revenue Cost of Revenue Contract with customer, revenue recognized Contract with Customer, Liability, Revenue Recognized Commitments and Contingencies Disclosure [Abstract] Commitments and Contingencies Disclosure [Abstract] Change in BIE Change in BIE Change in BIE from the prior year to the current period. Interest income Investment Income, Interest Document Transition Report Document Transition Report Document Quarterly Report Document Quarterly Report Entity Current Reporting Status Entity Current Reporting Status Line of credit facility, initiation date Line of Credit Facility, Initiation Date Retained Earnings Retained Earnings [Member] Additional margin on alternate base rate loans, minimum Line Of Credit Basis Spread On Alternate Base Rate Minimum Line of credit basis spread on alternate base rate minimum. AOCI Attributable to Parent AOCI Attributable to Parent [Member] Inventories Inventory, Net Weighted Average Number of Shares Outstanding, Basic Weighted average shares outstanding - basic (in shares) Weighted Average Number of Shares Outstanding, Basic Entity Address, State or Province Entity Address, State or Province Property, Plant and Equipment [Line Items] Property, Plant and Equipment [Line Items] Statement [Line Items] Statement [Line Items] Proceeds from asset sales Proceeds from Sale of Productive Assets Total stockholders' equity Balances, beginning Balances, ending Total stockholders' equity Equity, Including Portion Attributable to Noncontrolling Interest Increase (Decrease) in Stockholders' Equity [Roll Forward] Increase (Decrease) in Stockholders' Equity [Roll Forward] Unapproved change orders and claims Construction Contractor, Contract Cost, Subject to Uncertainty, Amount Liabilities and stockholders’ equity Liabilities and Equity [Abstract] Entity Filer Category Entity Filer Category Time and materials and other cost reimbursable contracts Time-and-Materials Contract [Member] Asset backed credit facility, adjusted term SOFR three-month tenor, basis points Asset Backed Credit Facility Adjusted Term SOFR Three Month Add On Asset Backed Credit Facility Adjusted Term SOFR Three Month Add On Burlington Office Burlington Office [Member] Burlington Office Remaining performance obligations yet to be satisfied Revenue, Remaining Performance Obligation, Amount Loss Contingencies [Line Items] Loss Contingencies [Line Items]