Applied Numerical Methods Using MATLAB, 2nd Edition

Appendix BMatrix Operations/Properties

Chapter Outline

• B.1 Addition and Subtraction
• B.2 Multiplication
• B.3 Determinant
• B.4 Eigenvalues and Eigenvectors of a Matrix ¹
• B.5 Inverse Matrix
• B.6 Symmetric/Hermitian Matrix
• B.7 Orthogonal/Unitary Matrix
• B.8 Permutation Matrix
• B.9 Rank
• B.10 Row Space and Null Space
• B.11 Row Echelon Form
• B.12 Positive Definiteness
• B.13 Scalar (Dot) Product and Vector (Cross) Product
• B.14 Matrix Inversion Lemma

B.1 Addition and Subtraction

(B.1.1)

(B.1.2)

B.2 Multiplication

(B.2.1)

B.2.2

1. (cf) For this multiplication to be done, the number of columns of A must equal the number of rows of B.
2. (cf) The commutative law does not hold for the matrix multiplication, i.e. AB ≠ BA.

B.3 Determinant

The determinant of a K × K (square) matrix A = [a_mn] is defined by

(B.3.1)

where the minor M_kn is the determinant of the (K − 1) × (K − 1) (minor) matrix formed by removing the kth row and the nth column from A and A_kn = (−1)^k + nM_kn is called ...