TRANSPOSE OF A MATRIX.
Given a matrix A of order mxn, the matrix AT is obtained by exchanging the rows of
A and its columns, this is called: THE TRANSPOSE OF MATRIX A.
Example: Thus, the transposition of
Orthogonal arrays
A real matrix A is said to be orthogonal, if AAT = AT A = I. Its observed that an
ortogonal matrix A is necessarily square and invertible, with inverse A-1 = AT.
Consider a matrix 3 ´ 3 arbitrary:
If A is orthogonal, then:
Normal Matrix
A matrix is normal if it commutes with its transpose, that is, if AAT = ATA. Obviously, if A
is symmetric, antisymmetric, or orthogonal, it is necessarily normal.
Example:
Puesto que AAT = ATA, la matriz es normal
