This Matrix Calculator will easily find the matrix determinant, the rank, find the sum and the multiplication of matrices, calculate the inverse matrix. Just type matrix elements and click the button.

An n × m matrix is an array of numbers with n rows and m columns. n and m are the dimensions of the matrix.

The addition and the subtraction of the matrices are carried out term by term. The matrices must have the same dimensions

Each term in the matrix is multiplied by the number

A^{T} transposed (also denoted by A') of a matrix A is the matrix obtained by interchanging the rows and columns of A

The transpose of a column vector is a row vector

first define the product of a row vector x^{T} by a column vector y
This product is called scalar product of vectors x and y, denoted x · y. The vectors must have the same dimension.

The matrix product is deduced: the product of the matrix A (n × m) of the matrix B (m × p) is the matrix C (n × p) such that the element C_{ij} is equal to the scalar product of the row i of matrix A through column j of matrix B.

In a square matrix A is invertible so-called regular or if there is a square matrix A^{-1} (called inverse matrix) such that:
A × A^{-1} = A^{-1} × A = I

The determinant is a scalar value that is a function of the inputs of a square matrix.

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