Matrix Functions (50)

Compute the characteristic polynomial det(lambda*I - A) of a square matrix using the Faddeev-LeVerrier algorithm. Returns an array of coefficients in ascending order [c_0, c_1, ..., c_n] where c_0 + c_1*lambda + ... + c_n*lambda^n.

Compute the Cholesky decomposition of a symmetric positive definite matrix A. Returns a lower triangular matrix L such that A = L * L^T.

Return a column from a matrix or array.

Concatenate matrices. By default, the matrices are concatenated by the last dimension. The dimension on which to concatenate can be provided as last argument.

Count the number of elements of a matrix, array or string.

Calculate the cross product for two vectors in three dimensional space.

Complex Conjugate and Transpose a matrix

Calculate the determinant of a matrix

Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned. When k is provided, the k-th diagonal will be filled in or retrieved,

Calculate the dot product of two vectors.

Calculate the eigenvalues and optionally eigenvectors of a square matrix

Calculate N-dimensional Fourier transform

Filter items in a matrix.

Flatten a multi dimensional matrix into a single dimensional matrix.

Iterates over all elements of a matrix/array, and executes the given callback function.

Find the data type of all elements in a matrix or array,

Reduce a square matrix A to upper Hessenberg form using Householder reflections. Returns an object { H, Q } where H is upper Hessenberg (zeros below the first subdiagonal) and Q is orthogonal, satisfying A = Q * H * Q^T.

Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.

Calculate N-dimensional inverse Fourier transform

Calculate the inverse of a matrix

Compute the Jordan normal form J of a square matrix A and a transition matrix P such that A = P * J * inv(P). For simple eigenvalues the result is diagonal; for repeated eigenvalues Jordan blocks with 1s on the superdiagonal are constructed.

Calculates the Kronecker product of 2 matrices or vectors.

Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array or the matrices/arrays.

Generate a matrix one dimension less than A by applying callback to

Create a dense matrix from vectors as individual columns.

Create a matrix by evaluating a generating function at each index.

Create a dense matrix from vectors as individual rows.

Compute the principal matrix logarithm of a square matrix A using eigendecomposition. Returns L such that expm(L) ≈ A. Requires that A has strictly positive real eigenvalues.

Raise a square matrix A to an integer power n. For n > 0 uses binary exponentiation (repeated squaring). For n = 0 returns the identity matrix. For n < 0 returns inv(A)^|n|.

Compute the numerical rank of a matrix using Singular Value Decomposition. The rank is the number of singular values exceeding a threshold tolerance.

Compute an orthonormal basis for the null space (kernel) of a matrix A using Singular Value Decomposition. Returns an array of basis vectors corresponding to near-zero singular values.

Create a matrix containing ones.

Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.

Calculate the Moore–Penrose inverse of a matrix

Compute the polar decomposition A = U * P of a square matrix A, where U is an orthogonal (unitary) matrix and P is a symmetric positive semidefinite matrix. Computed via SVD: A = U_svd * diag(S) * V^T, then U = U_svd * V^T and P = V * diag(S) * V^T.

Reshape a multi dimensional array to fit the specified dimensions.

Resize a matrix.

Returns a 2-D rotation matrix (2x2) for a given angle (in radians).

Returns a 2-D rotation matrix (2x2) for a given angle (in radians).

Return a row from a matrix or array.

Compute the Reduced Row Echelon Form (RREF) of a matrix using Gauss-Jordan elimination with partial pivoting. Each pivot element is scaled to 1, and all other entries in the pivot column are eliminated.

Calculate the size of a matrix.

Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.

Remove inner and outer singleton dimensions from a matrix.

Get or set a subset of the entries of a matrix or

Compute the Singular Value Decomposition A = U * diag(S) * V^T, returning an object { U, S, V } where U and V are orthogonal matrices and S is a vector of non-negative singular values in descending order.

Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.

Transpose a matrix

Create a matrix containing zeros.