sanic (version 0.0.2)

eigen2: Spectral Decomposition

Description

Solvers for eigenproblems around the matrix \(A\). Compute eigenvalues \(\lambda\) and eigenvectors \(v\) of \(A\), such that \(Av = \lambda v\).

Usage

eigen2(a, symmetric, vectors = TRUE)

Value

Solves the eigenproblem and returns a list with eigenvalues in the "values" slot and, if requested, eigenvectors in the slot "vectors".

Arguments

a

Square numeric matrix.

symmetric

Logical scalar indicating whether 'a' is symmetric. By default symmetry is checked up to machine precision, which may take a long time for symmetric matrices.

vectors

Logical scalar indicating whether eigenvectors should be computed and returned.

Examples

set.seed(42)
# Compute eigenvalues and eigenvectors for a square matrix
A <- matrix(rnorm(9), nrow = 3, ncol = 3)
ev <- eigen2(A, symmetric = FALSE)

# Compute eigenvalues and eigenvectors for a symmetric matrix
A <- crossprod(matrix(rnorm(9), nrow = 3, ncol = 3))
ev <- eigen2(A, symmetric = TRUE)
# Check reconstruction
norm(A %*% ev$vectors - ev$vectors %*% diag(ev$values))