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Assuming "matrices" is a general topic | Use as a computation or referring to a mathematical definition or a word instead
Mathematics
Matrices & Linear Algebra

Matrix Arithmetic

do basic arithmetic on matrices

{{0,-1},{1,0}}.{{1,2},{3,4}}+{{2,-1},{-1,2}}

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

Matrix Operations

compute properties of a matrix

{{6, -7, 10}, {0, 3, -1}, {0, 5, -7}}

compute the rank of a matrix

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

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)

compute the adjugate of a matrix

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

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}}

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}}

Diagonalization

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}}

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

Vector Spaces

compute the row space of a matrix

row space {{1,2,-5},{-1,0,-1},{2,1,-1}}

compute the column space of a matrix

{{1,0,-1},{2,-1,3}} column space

compute the null space of a matrix

null space of {{1,0,-2,1},{2,-1,1,0},{0,2,-3,1}}

Linear Independence

determine whether a set of vectors is linearly independent

Are (2,-1) and (4,2) linearly independent?

linear independence (1,3,-2), (2,1,-3), (-3,6,3)

specify complex vectors

are (1,i), (i,-1) linearly independent?

specify vectors with one or more symbolic components

linear independence of {(1,3,-1), (-1,-5,5), (4,7,h)}

linear independence (a,b,c,d), (e,f,g,h), (i,j,k,l)

 
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