definiteness: Definiteness of a 2D real-valued matrix
In PhilippVWC/myBayes: Functions for time series analysis based on Bayesian methods

Description Usage Arguments Details Value Author(s) Examples

This routine checks the definiteness of a two dimensional, real-valued matrix.

1	definiteness(x)

`x`	matrix of type double - A real-valued, 2D matrix.

This routine takes the symmetric part of the given matrix and decomposes its spectrum to find an answer.

character string - A character string indicating the definiteness of the given matrix.

Philipp van Wickevoort Crommelin

# positive definite
A = matrix(data = c(1,0,0,0,7,0,0,0,2),
           ncol = 3)
definiteness(A)

# negative definite
definiteness(-A)

# positive semi-definite
A = matrix(data = c(1,0,0,0,0,0,0,0,2),
           ncol = 3)
definiteness(A)

# negative semi-definite
definiteness(-A)

# Example, that demonstrates the importance of symmetry of the given matrix:
B = matrix(data = c(4,1,9,4),
           ncol = 2) #Eigenvalues all positive but not symmetric
definiteness(B)
eigen(B)$values
# Scalar product maps to negative value
v = c(-1,1)
t(v)%*%B%*%v