Nhalf_power: The Negative Half Power of a Matrix

In XiulinXie/SPCmonitor2: Process Control Chart for Monitoring Short-Range Serially Correlated Data

Description

This function computes negative half power of a square matrix x based on eigenvectors and eigenvalues.

Usage

Nhalf_power(x)

Arguments

x

matrix

Details

The Negative Half Matrix power is computed by eigenvectors and eigenvalues. X^(-1/2) = UΛ^(-1/2)U* where X is a hermitian matrix, 𝑈 is a unitary matrix with columns the eigenvectors of matrix X, 𝑈∗ is the conjugate transpose of matrix 𝑈 and Λ is a diagonal matrix with entries the eigenvalues of matrix X. If the negative half power of input matrix does not exist, the result matrix might have NaN.

Value

x^(-1/2)

Author(s)

Xiulin Xie

Examples

Nhalf_power(matrix(c(1, 0.4, 0.4, 1), nrow = 2))

XiulinXie/SPCmonitor2 documentation built on Dec. 10, 2019, 12:10 a.m.