rank matrix
Assuming the input is a general topic | Use as or instead | Use "matrix" as

Examples forMatrices

Matrix Properties

Calculate properties of a matrix:

{{6, -7}, {0, 3}}
{{1, -5, 8}, {1, -2, 1}, {2, -1, -5}}

Matrix Arithmetic

Add matrices:

{{1, 2}, {3, 4}} + {{2, -1}, {-1, 2}}

Multiply matrices:

{{2, -1}, {1, 3}} . {{1, 2}, {3, 4}}

Matrix vector product:

{{2, -1, 1}, {0, -2, 1}, {1, -2, 0}} . {x, y, z}

Trace

Compute the trace of a matrix:

tr {{9, -6, 7}, {-9, 4, 0}, {-8, -6, 4}}
tr {{a, b}, {c, d}}

Determinant

Compute the determinant of a matrix:

determinant of {{3, 4}, {2, 1}}
det({{9, 3, 5}, {-6, -9, 7}, {-1, -8, 1}})
det {{a, b, c}, {d, e, f}, {g, h, j}}

Minors

Calculate a minor of a matrix:

(1,2)-minor of {{1,2,3},{3,4,5},{5,4,3}}
M-23 of {{2, a, 5, b}, {7, c+d, 9, 11}, {13, 17, 19, 23}, {a-1, -2, b+c, 4}}

Inverse

Compute the inverse of a matrix:

inv {{10, -9, -12}, {7, -12, 11}, {-10, 10, 3}}
inverse {{a, b}, {c, d}}
{{2, 3}, {4, 5}}^(-1)

Find a pseudoinverse:

inverse {{1, -4, 3}, {2, -5, 8}}

Row Reduction

Row reduce a matrix:

row reduce {{2, 1, 0, -3}, {3, -1, 0, 1}, {1, 4, -2, -5}}
row reduction calculator

Eigenvalues & Eigenvectors

Compute the eigenvalues of a matrix:

eigenvalues {{4, 1}, {2, -1}}

Compute the eigenvectors of a matrix:

eigenvectors {{1, 0, 0}, {0, 0, 1}, {0, 1, 0}}

Compute the characteristic polynomial of a matrix:

characteristic polynomial {{4, 1}, {2, -1}}

Other Matrix Operations

Compute the transpose of a matrix:

transpose {{-3, 2}, {5, 1}}

Compute the rank of a matrix:

rank {{6, -11, 13}, {4, -1, 3}, {3, 4, -2}}

Compute the nullity of a matrix:

nullity {{6, -11, 13}, {4, -1, 3}, {3, 4, -2}}

Compute the adjugate of a matrix:

adjugate {{8, 7, 7}, {6, 9, 2}, {-6, 9, -2}}

Compute the minors of a matrix:

minors {{1, 2, 3}, {3, 2, 1}, {2, 1, 3}}
Matrix Decompositions »

Diagonalize a matrix:

diagonalize {{1, 2}, {3, 4}}

Compute the LU decomposition of a square matrix:

LU decomposition of {{7, 3, -11}, {-6, 7, 10}, {-11, 2, -2}}

Compute a singular value decomposition:

SVD {{1, 0, -1}, {-2, 1, 4}}
Geometric Transformations »

Compute a 2 x 2 rotation matrix:

rotate 30 degrees

Compute a 3 x 3 reflection matrix:

reflect across x + y + z = 1

Types of Matrices

Determine whether a matrix has a specified property:

Is {{3, -3}, {-3, 5}} positive definite?

Get information about a type of matrix:

Hilbert matrices
Hankel matrices

Specify a size:

5x5 Hilbert matrix

Have a question about using Wolfram|Alpha?Contact Pro Premium Expert Support »

Give us your feedback »