# Matrix Calculator

Matrix A

Matrix B

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.

## Matrix

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

## Matrix multiplication by a number

Each term in the matrix is multiplied by the number

## Transpose of a matrix

AT 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

## Matrix multiplication

first define the product of a row vector xT 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 Cij is equal to the scalar product of the row i of matrix A through column j of matrix B.

## Inverse of a matrix

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

## Determinant of a matrix

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