Matrices : Reminder

Definition of a matrix

A matrix of dimension n*p is an array of numbers with n rows and p columns. These numbers are called the coefficients of the matrix. We note that `a_(ij)` is the coefficient of row i and column j.

Operations on matrices

Sum of matrices

The sum of two matrices M and N of the same dimension is the matrix obtained by adding the coefficients in the same positions. This matrix is labelled M+N and can be calculated using the matrix calculator.

Products of matrices

The product of two matrices A of dimension (m,n) and B of dimension (n,p) is the matrix C of dimension (m,p).
If we note that `A(a_(ij))`, `A(b_(ij))`, `C(c_(ij))` then the coefficients of the matrix C are calculated using the following formula: `c_(ij)=sum_(k=1)^p(a_(ik)*b_(kj))`.
The matrix product calculator can determine the result.

Transposing a matrix

Given a matrix M(n,p), where n is the number of rows and p is the number of columns, the transpose of the matrix M(n,p) is the matrix obtained by swapping the rows and columns. It can be calculated using the transpose calculator.

Inversion of a square matrix

The matrix A is said to be invertible if there exists a matrix B of order n such that AB = BA = I, where I is the unit matrix. The inverse of the matrix A is denoted by `A^-1` and can be obtained using the inverse matrix calculator.

Determinant of a square matrix

The determinant of the square matrix of order n `A=(a_(ij))`, matrice carrée d'ordre n, is the determinant of the column vectors of the matrix. The matrix determinant calculator is able to find this type of result.