Matrix Calculator: Inverse, Determinant & Operations
Add or multiply matrices, transpose A, calculate its determinant or follow a Gauss–Jordan inverse with every elementary row operation. Enter dimensions and values locally in your browser.
About this matrix calculator: inverse, determinant & operations
Add or multiply matrices, transpose A, calculate its determinant or follow a Gauss–Jordan inverse with every elementary row operation. Enter dimensions and values locally in your browser Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
The execution engine processes input tokens and applies transformations in the browser sandbox. Specifically, Addition is cellwise; product[i,j]=Σₖ a[i,k]×b[k,j]; transpose swaps indices. Determinant uses elimination; inverse uses Gauss–Jordan on [A | I].
Worked numerical calculation
Scenario: Inverse of A
Sample input:
Processing: Choose the operation, dimension range and sizes of A and, when needed, B. For A=[[1,2],[3,4]], det(A)=−2 and inverse(A)=[[-2,1],[1.5,-0.5]]. Multiplying A by this inverse gives the identity matrix.
Illustrative output:
Domain range & precision boundaries
Standard input supports 1–6 rows and columns. Extended mode supports 1–8, matching the separate computational ceiling. Returning to standard mode removes rows or columns beyond 6. Native binary64 arithmetic may round or underflow. Nonfinite intermediate values or results are rejected. Inversion uses scaled partial pivoting: a zero pivot is singular; a pivot no larger than n × Number.EPSILON times its original row scale is rejected as numerically unstable. This is not exact symbolic algebra. A determinant can underflow to zero or overflow; inverse availability is decided from pivots, not the rounded determinant. The residual is a check, not an accuracy guarantee. Calculation is local, offline after loading, without an external computation service, paid dependency or required output file.
Calculations in Matrix Calculator: Inverse, Determinant & Operations use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in Matrix Calculator: Inverse, Determinant & Operations run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Matrix Calculator: Inverse, Determinant & Operations verification · Audit standards
How to use it
- Enter, paste, or select your input data into the Matrix Calculator: Inverse, Determinant & Operations workspace controls.
- Enter finite decimal cells. Addition needs equal shapes; multiplication needs matching inner dimensions; determinant and inverse need square A.
- Calculate, inspect the complete result and follow the row operations for determinant or inverse. Editing any input clears the old result.
Frequently asked questions
Which matrix operations are supported?+
Addition is cellwise; product[i,j]=Σₖ a[i,k]×b[k,j]; transpose swaps indices.
What dimensions and numeric limits apply?+
Boundary constraints concerning "What dimensions and numeric limits apply?" prevent invalid parameter state mutations client-side.
How can I check an inverse?+
Runtime handling of "How can I check an inverse?" executes synchronously in your browser tab without remote delays.
Where are my matrices processed?+
Security isolation for "Where are my matrices processed?" ensures zero transmission beyond your local workstation.