From AIMSWiki

Functions

• det(A) computes the determinant of the matrix A.
• lambda = eig(A) returns the eigenvalues of A in lambda, and
• [V, lambda] = eig(A) also returns the eigenvectors in V.
• inv(A) computes the inverse of matrix A. Note that calculating the inverse is often 'not' necessary. See the next two operators as examples.
• A / B computes X such that XB = A. This is called right division and is done without forming the inverse of B.
• A \ B computes X such that AX = B. This is called left division and is done without forming the inverse of A.
• norm(A, p) computes the p-norm of the matrix (or vector) A. The second argument is optional with default value p = 2.
• rank(A) computes the (numerical) rank of a matrix.
• trace(A) computes the trace (sum of the diagonal elements) of A.
• expm(A) computes the matrix exponential of a square matrix. This is defined as

• logm(A) computes the matrix logarithm of a square matrix.
• sqrtm(A) computes the matrix square root of a square matrix.

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Below are some more linear algebra functions. Use help to find out more about them.

• balance (eigenvalue balancing),
• cond (condition number),
• dmult (computes diag(x) * A efficiently),
• dot (dot product),
• givens (Givens rotation),
• kron (Kronecker product),
• null (orthonormal basis of the null space),
• orth (orthonormal basis of the range space),
• pinv (pseudoinverse),
• syl (solves the Sylvester equation).

Factorizations

• R = chol(A) computes the Cholesky factorization of the symmetric positive definite matrix A, i.e. the upper triangular matrix R such that R^TR = A.
• [L, U] = lu(A) computes the LU decomposition of A, i.e. L is lower triangular, U upper triangular and A = LU.
• [Q, R] = qr(A) computes the QR decomposition of A, i.e. Q is orthogonal, R is upper triangular and A = QR.

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Below are some more available factorizations. Use help to find out more about them.

• qz (generalized eigenvalue problem: QZ decomposition),
• qzhess (Hessenberg-triangular decomposition),
• schur (Schur decomposition),
• svd (singular value decomposition),
• housh (Householder reflections),
• krylov (Orthogonal basis of block Krylov subspace).

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