Matrix Multiplication Calculator
Matrix Multiplication Calculator: Computes row-by-column dot products: [1*5+2*7, 1*6+2*8; 3*5+4*7, 3*6+4*8].
About this matrix multiplication calculator
Matrix Multiplication & Inverse Calculator — browser-based utility.
How this tool works
Calculation and parameter relationship: product[i,j]=Σₖ a[i,k]×b[k,j]
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Worked example
Scenario: Multiply a 2×3 numeric matrix by a 3×2 numeric matrix.
Sample input:
Processing: Each product cell is a three-term dot product; collect the two rows and two columns.
Illustrative output:
Limits and verification
Parameter domains and units: a:m×n; b:n×p; product:m×p; m,n,p ∈ ℤ; m,n,p ≥ 1. Results use binary64 floating-point numbers unless BigInt is stated. Result cards show up to 10 significant digits; raw output retains the serialized value. A null ratio means the model has no meaningful finite value for that ratio; it is not zero.
Examples demonstrate an expected workflow; they do not prove every input or every branch of an external specification. Check important results with an independent source before using them for money, security, compliance, safety, or irreversible file changes.
Browser processing boundary
Tool input is processed by code running in the browser and is not intentionally sent to a CZOA processing API. The page can still request ordinary site assets, analytics, or advertising when those services are enabled. Browser extensions and managed-device software remain outside this tool's control.
Relevant references
These references govern or help explain the format, protocol, or calculation used here. Listing a reference does not claim certification or complete implementation of every optional feature.
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Content owner: CZOA Tools · Last reviewed: 2026-09-15 · Review methodology
How to use it
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Frequently asked questions
How does the matrix calculator form each output cell?+
For each output row i and column j it sums a[i][k] × b[k][j] over the shared inner dimension k. It returns JSON with product only; it does not compute determinants, inverses, or elementwise products.
What JSON matrix structure is accepted?+
Provide {"a":[[...]],"b":[[...]]}. Both values must be nonempty rectangular arrays of finite JavaScript numbers. The number of columns in a must equal the number of rows in b.
What matrix dimension and precision boundaries apply?+
An m×n left matrix can multiply only an n×p right matrix, yielding m×p. The implementation uses Number multiplication and addition, so decimal inputs follow binary64 rounding; it is not a symbolic or BigInt matrix calculator.
What did the independent browser vector return?+
For a=[[2,-1,3],[0,4,5]] and b=[[1,2],[3,0],[-2,1]], the exact output was product=[[-7,7],[2,5]]. The browser fixture used the raw JSON control and local execution.