Special Type of Matrix

i. Orthogonal matrix A square matrix A is called an orthogonal matrix if the product of matrix A and its transpose A' (or AT) is an identity matrix, i.e. AA'=

Note if A and B are orthogonal, then AB is also orthogonal 2. Conjugate of a matrix The matrix obtained from

any given matrix A containing complex numbers as its elements, on replacing its elements by the corresponding conjugate complex numbers is called conjugate of A and is denoted by Ā. .

e.g. If

[1+2i 2-3i A 4–5 i 5+6 il 5

[1 – 2i 2+ 3i then Ā

4+5 i 5-6 i

3. Hermitian matrix A square matrix such that

(A')= A, then A is known as hermitian matrix.

4. Skew-hermitian matrix A square matrix such that (Ā')=- A, then A is known as skew-hermitian matrix.

5. Elementary matrix A square matrix is called an elementary matrix if it can be obtained from identit matrix I by performing single elementary row or column operation.