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Matrix Calculator

Paste your matrices below. Separate values with spaces or commas, and put each row on a new line. Choose an operation and click Calculate.

Binary operations (add, subtract, multiply) require both A and B. Unary operations (determinant, transpose, inverse, rank) use only the selected matrix.

Example A (2×3): 1 2 3\n4 5 6

Provide Matrix B for add/subtract/multiply, or when selecting determinant/transpose/inverse/rank of B.

Controls rounding in the output (0–10 decimal places).

The Matrix Calculator lets you add, subtract, multiply, transpose, find determinants, compute inverses, and evaluate ranks of matrices in seconds. Paste your matrices, choose an operation, and get accurate, rounded results instantly.

Why use this Matrix Calculator?

Working with matrices is central to linear algebra, data science, computer graphics, engineering, and more. Yet, manual calculations can be tedious and error-prone, especially for larger matrices. This Matrix Calculator streamlines the process by handling common operations with reliable numerical methods and clear output formatting. Whether you are a student checking homework, a researcher validating a derivation, or a developer prototyping an algorithm, this tool saves time while improving accuracy.

Supported operations

  • Addition (A + B) and Subtraction (A ? B) for matrices of the same size.
  • Multiplication (A × B) when the number of columns in A matches the number of rows in B.
  • Transpose (A^T or B^T) to flip rows and columns.
  • Determinant for square matrices, useful for invertibility, volume scaling, and system properties.
  • Inverse for non-singular square matrices using Gauss–Jordan elimination with partial pivoting.
  • Rank via row-reduction to understand linear independence and matrix dimension.

How to input matrices

Enter each row on a new line and separate values with spaces or commas. For example, a 2×3 matrix can be entered as: "1 2 3" on the first line and "4,5,6" on the second line. The calculator automatically detects the matrix size based on your input. For binary operations like addition and multiplication, provide both Matrix A and Matrix B. For unary operations like determinant or transpose, you only need the relevant matrix.

Precision and formatting

Use the precision control to set how many decimal places you want in the result. This is particularly helpful for results that involve divisions or floating-point arithmetic, such as inverses and determinants. Internally, the calculator uses stable numerical techniques, including partial pivoting for elimination, to improve robustness against rounding errors.

Common use cases

  • Check homework: Verify addition, subtraction, and multiplication results quickly.
  • Linear systems insight: Evaluate determinants and rank to assess solvability and dependence.
  • Data transformations: Use the inverse and transpose for coordinate changes and orthogonalization.
  • Algorithm prototyping: Validate intermediate matrix steps in optimization and machine learning workflows.

Tips for accurate results

  • Ensure each matrix row has the same number of values.
  • For multiplication, verify A’s columns equal B’s rows.
  • Determinant and inverse require square matrices; singular matrices have no inverse.
  • Increase precision if your results involve small pivots or near-singular matrices.

Get started

Paste your matrices, choose an operation, and click Calculate. The Matrix Calculator will parse your input, validate dimensions, perform the computation, and display the result in a clean, readable format. If anything is inconsistent—like mismatched sizes or a singular matrix—you’ll receive a clear error message explaining what went wrong and how to fix it.

FAQs

What operations does the Matrix Calculator support?

The Matrix Calculator supports addition, subtraction, multiplication, transpose, determinant, inverse, and rank.

How should I format inputs for the Matrix Calculator?

Enter each row on a new line and separate numbers with spaces or commas. The Matrix Calculator detects size automatically.

Can the Matrix Calculator find the inverse of any matrix?

It computes inverses for square, non-singular matrices. If a matrix is singular, the Matrix Calculator will let you know.

Does the Matrix Calculator handle non-square matrices?

Yes. Non-square matrices are valid for addition, subtraction (same size), multiplication (A cols = B rows), transpose, and rank.

What does the precision setting do in the Matrix Calculator?

Precision sets decimal places in the output, useful for operations like inverse and determinant involving floating-point arithmetic.

Why does the Matrix Calculator say my matrices are incompatible?

Likely a size mismatch: add/subtract need same size; multiply needs A columns equal to B rows; determinant/inverse need square matrices.

Can I compute the determinant of Matrix B with the Matrix Calculator?

Yes. Select the B-specific determinant option and paste Matrix B; the Matrix Calculator will compute det(B).

Is the Matrix Calculator suitable for large matrices?

It works for typical coursework sizes. Very large matrices may be slower due to the intensive arithmetic involved.

Does the Matrix Calculator show steps?

It shows results with clear formatting. For learning, you can adjust precision or try intermediate operations like transpose and rank.