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#' Test for a Positive Definite Matrix
#'
#' Returns `TRUE` if input
#' is a positive definite matrix,
#' and `FALSE` otherwise.
#'
#' A
#' \eqn{k \times k}
#' symmetric matrix
#' \eqn{\mathbf{A}}
#' is positive definite
#' if all of its eigenvalues are positive.
#'
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @param eigen output of the [eigen()] function.
#' @param tol Numeric.
#' Tolerance.
#'
#' @references
#' [Wikipedia: Definite matrix](https://en.wikipedia.org/wiki/Definite_matrix)
#'
#' @return Logical.
#'
#' @family Linear Algebra Functions
#' @keywords linearAlgebra test internal
#' @noRd
.TestPositiveDefinite <- function(eigen,
tol = 1e-06) {
return(
all(
eigen$values >= -tol * abs(
eigen$values[1L]
)
)
)
}
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