Linear Algebra Calculators

Vector Dot (Inner) Product Calculator

An online calculator for finding the dot (inner) product of two vectors, with steps shown.

Vector Magnitude Calculator

An online calculator for finding the magnitude (length) of a vector, with steps shown.

Angle between Vectors Calculator

The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work.

Scalar Projection Calculator

The calculator will find the scalar projection of one vector onto another, with steps shown.

Vector Projection Calculator

The calculator will find the vector projection of one vector onto another, with steps shown.

Gram-Schmidt Calculator

This calculator will orthonormalize the set of vectors using the Gram-Schmidt process, with steps shown.

Cross Product Calculator

An online calculator for finding the cross product of two vectors, with steps shown.

Matrix Transpose Calculator

The calculator will find the transpose of the given matrix, with steps shown.

Trace of Matrix Calculator

The calculator will find the trace of the matrix, with steps shown.

Reduced Row Echelon Form (RREF) Caclulator

The calculator will find the row echelon form (simple or reduced - RREF) of the given (augmented) matrix (with variables if needed), with steps shown.

Gauss-Jordan Elimination Calculator

The calculator will perform the Gaussian elimination on the given augmented matrix, with steps shown. Complete reduction is available optionally.

Rank of Matrix Calculator

The calculator will find the rank of the matrix, with steps shown.

Row Space of Matrix Calculator

The calculator will find the row space of the matrix, with steps shown.

Column Space of Matrix Calculator

The calculator will find the column space of the matrix, with steps shown.

Matrix Null Space and Nullity Calculator

The calculator will find the null space and the nullity of the given matrix, with steps shown.

Matrix Determinant Calculator

The calculator will find the determinant of the matrix (2x2, 3x3, 4x4 etc.) using the cofactor expansion, with steps shown.

Inverse of Matrix Calculator

The calculator will find the inverse of the square matrix using the Gaussian elimination method, with steps shown.

Matrix of Minors Calculator

The calculator will find the matrix of minors of the given square matrix, with steps shown.

Cofactor Matrix Calculator

The calculator will find the matrix of cofactors of the given square matrix, with steps shown.

Adjugate Matrix Calculator

The calculator will find the adjugate (adjoint, adjunct) matrix of the given square matrix, with steps shown.

Characteristic Polynomial Calculator

The calculator will find the characteristic polynomial of the given matrix, with steps shown.

Eigenvalues and Eigenvectors Calculator

The calculator will find the eigenvalues and eigenvectors (eigenspace) of the given square matrix, with steps shown.

Diagonalize Matrix Calculator

The calculator will diagonalize the given matrix, with steps shown.

Matrix Addition Calculator

The calculator will find the sum of two matrices (if possible), with steps shown. It adds matrices of any size up to 10x10 (2x2, 3x3, 4x4 etc.).

Matrix Subtraction Calculator

The calculator will find the difference of two matrices (if possible), with steps shown. It subtracts matrices of any size up to 10x10 (2x2, 3x3, 4x4 etc.).

Matrix Scalar Multiplication Calculator

The calculator will multiply the given matrix by the given scalar, with steps shown. It handles matrices of any size up to 10x10 (2x2, 3x3, 4x4 etc.).

Matrix Multiplication Calculator

The calculator will find the product of two matrices (if possible), with steps shown. It multiplies matrices of any size up to 10x10 (2x2, 3x3, 4x4 etc.).

Matrix Division Calculator

The calculator will find the quotient of two matrices (if possible), with steps shown. It divides matrices of any size up to 7x7 (2x2, 3x3, 4x4 etc.).

Matrix Power Calculator

The calculator will find raise the given matrix to the given integer (positive or negative) power (if possible), with steps shown. It handles matrices of any size up to 7x7 (2x2, 3x3, 4x4 etc.).

Matrix Calculator

This solver will add, subtract, multiply, divide, and raise to power two matrices, with steps shown. It will also find the determinant, inverse, rref (reduced row echelon form), null space, rank, eigenvalues and eigenvectors.