The left polar decomposition.

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Description

polar calculates the left polar decomposition of a matrix.

Usage

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polar(X)

Arguments

X

A matrix.

Details

polar Takes a matrix X, of dimensions n by p, and returns two matrices P and Z such that X = PZ. P is a symmetric positive definite matrix of dimension n by n and Z is an n by p matrix with orthonormal rows.

Value

P A n by n symmetric positive definite matrix.

Z A n by p matrix with orthonormal rows.

Note that X == P %*% Z, up to numerical precision.

Author(s)

David Gerard.

Examples

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X <- matrix(1:6, nrow = 2)
polar_x <- polar(X)
P <- polar_x$P
Z <- polar_x$Z
P
Z
trim(Z %*% t(Z))
trim(X - P %*% Z)

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