Last updated: August 1, 2026
Matrix Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Enter Matrix A, choose the matrix operation you want, and then provide Matrix B, a scalar, an exponent, or a norm type only when that operation needs it. The calculator handles determinant, transpose, trace, rank, norm, power, scalar multiplication, addition, subtraction, and multiplication in one place.
Enter Matrix A, choose the operation you want, and then add Matrix B, a scalar, or an exponent only when that operation needs it.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
Choose an operation such as det(A), tr(A), rank(A), Aᵀ, Aⁿ, kA, A ± B, or AB.
Where:
- A=primary matrix
- B=secondary matrix for binary operations
- k=scalar
- n=non-negative integer exponent
Worked Examples
Determinant mode
Compute det([[1,2],[3,4]]).
- 1Choose determinant.
- 2Enter Matrix A.
- 3Read the scalar result.
Addition mode
Add two 2×2 matrices.
- 1Choose add.
- 2Enter Matrix B with the same shape.
- 3Combine entries position by position.
Norm mode
Measure the Frobenius norm of a small matrix.
- 1Choose norm.
- 2Keep Matrix B empty.
- 3Read the numeric norm value.
Power mode
Square a 2×2 matrix.
- 1Choose power.
- 2Set exponent to 2.
- 3Multiply the matrix by itself.
Introduction
Use one workspace for determinant, transpose, trace, rank, norm, power, scalar multiplication, addition, subtraction, and multiplication.
Overview
Use one workspace for determinant, transpose, trace, rank, norm, power, scalar multiplication, addition, subtraction, and multiplication.
Primary result
Quick matrix exploration
Homework verification
Switching between scalar and matrix summaries
Input format
Use rows separated by semicolons, such as 1,2;3,4.
Separate rows with semicolons
Separate entries with commas or spaces
Brackets are optional
Keep row lengths consistent
Formula and method
Choose an operation such as det(A), tr(A), rank(A), Aᵀ, Aⁿ, kA, A ± B, or AB.
- A matters:
primary matrix.
- B matters:
secondary matrix for binary operations.
- K matters:
scalar.
- N matters:
non-negative integer exponent.
Validation rules
The calculator uses deterministic validation before it computes the final result.
Addition and subtraction require identical dimensions
Multiplication requires columns of A to match rows of B
Power requires a square matrix and a non-negative integer exponent
Determinant and trace require a square matrix
Interpreting the outputs
Use the main result first, then the secondary fields to verify the structure and meaning of the answer.
primaryResult holds the main answer
secondaryResult echoes dimensions, exponent, or norm type context
summary tells you exactly what was computed
Matrix outputs stay serialized in row format
Common use cases
These are typical reasons to use this calculator in study or applied work.
Quick matrix exploration
Homework verification
Switching between scalar and matrix summaries
Testing several operations on the same matrix
FAQs
What matrix format should I use?
Use rows separated by semicolons and entries separated by commas or spaces.
When do I need Matrix B?
Only for addition, subtraction, and multiplication.
When does the scalar field matter?
Only for scalar multiplication.
When does the exponent field matter?
Only for matrix power, and it must be a non-negative integer.
Which norm types are supported?
The calculator supports Frobenius, 1-norm, and infinity norm.
Why did an operation fail?
The most common reasons are malformed input, shape mismatches, or a square-matrix requirement.