Performs various linear algebra operations like finding the inverse, the QR decomposition, the eigenvectors and the eigenvalues.

columnspace(x, matrix = TRUE)

nullspace(x, matrix = TRUE)

rowspace(x, matrix = TRUE)

singular_values(x)

inv(x, method = c("gauss", "lu", "cf", "yac"))

eigenval(x)

eigenvec(x)

GramSchmidt(x)

pinv(x)

rref(x)

QRdecomposition(x)

LUdecomposition(x)

# S3 method for caracas_symbol
chol(x, ...)

svd_(x, ...)

det(x, ...)

trace_(x)

## Arguments

x

A matrix for which a property is requested.

matrix

When relevant should a matrix be returned.

method

The default works by Gaussian elimination. The alternatives are $LU$ decomposition (lu), the cofactor method (cf), and Ryacas (yac).

...

Auxillary arguments.

## Value

Returns the requested property of a matrix.

do_la()

## Examples

if (has_sympy()) {
A <- matrix(c("a", "0", "0", "1"), 2, 2) |> as_sym()

QRdecomposition(A)
LUdecomposition(A)
#chol(A) # error
chol(A, hermitian = FALSE)
eigenval(A)
eigenvec(A)
inv(A)
det(A)

## Matrix inversion:
d <- 3
m <- matrix_sym(d, d)
print(system.time(inv(m)))                  ## Gauss elimination
print(system.time(inv(m, method="cf")))     ## Cofactor
print(system.time(inv(m, method="lu")))     ## LU decomposition
if (requireNamespace("Ryacas")){
print(system.time(inv(m, method="yac")))  ## Use Ryacas
}

A <- matrix(c("a", "b", "c", "d"), 2, 2) %>% as_sym()
evec <- eigenvec(A)
evec
evec1 <- evec[[1]]$eigvec evec1 simplify(evec1) lapply(evec, function(l) simplify(l$eigvec))

A <- as_sym("[[1, 2, 3], [4, 5, 6]]")
pinv(A)
}
#>    user  system elapsed
#>   0.714   0.000   0.714
#>    user  system elapsed
#>   0.032   0.000   0.032
#>    user  system elapsed
#>   0.196   0.000   0.196