# Random Colors

Crude Java and Agile thoughts

## Matrices Basics

In a (m x n) matrix, m is the number of rows, n is the number of columns.

Two matrices ( a x b ) and ( c x d ) can be multiplied only if b == c.

(m x n) multiply (n x p) will result into a (m x p) matrix

Only square matrices can be inverted. Inversion is a tedious numerical procedure. Guass jordan method is a popular method to matrix inversion.

A x A(inverse) = Ainverse) x A = I ( where I is an identity matrix, it is a special case of diagonal matrix where all diagonal elements are 1 ).

If a determinant has a nonzero value, its matrix is described as regular and that if a determinant has zero value, its matrix is described as singular.

Associated with any square matrix is a single number that represents a unique function of the numbers in the matrix. this scalar function of a square matrix is called the determinant. the determinant of a matrix a is denoted by |a|.

If the determinant of the (square) matrix is exactly zero, the matrix is said to be singular and it has no inverse.

Symmetric matrix means that the matrix and its transpose are identical (i.e., a = a’).

If a matrix m is orthogonal then M x M(transpose) = M(transpose) x M = I = 1

where I is the identity matrix. but, we know that M x M(inverse) = I = 1. consequently, M(transpose) = M(inverse) ( for orthogonal matrices ). A variance-covariance matrix is used for representing a multivariate vector of p elements. the determinant of of variance-covariance matrix, is sometimes called the generalized variance.