Examples for

A matrix is a two-dimensional array of values that is often used to represent a linear transformation or a system of equations. Matrices have many interesting properties and are the core mathematical concept found in linear algebra and are also used in most scientific fields. Matrix algebra, arithmetic and transformations are just a few of the many matrix operations at which Wolfram|Alpha excels.

Explore various properties of a given matrix.

Calculate the trace or the sum of terms on the main diagonal of a matrix.

Reduce a matrix to its reduced row echelon form.

Find the diagonalization of a square matrix.

Find information on many different kinds of matrices.

Add, subtract and multiply vectors and matrices.

Calculate the determinant of a square matrix.

Calculate the eigensystem of a given matrix.

Transform a matrix into a specified decomposition.

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Invert a square invertible matrix or find the pseudoinverse of a non-square matrix.

Perform various operations, such as conjugate transposition, on matrices.

Find matrix representations for geometric transformations.