Electronic Circuits with MATLAB, PSpice, and Smith Chart

Appendix BMatrix Operations with MATLAB

B.1 Addition and Subtraction

(B.1a)

(B.1b)

B.2 Multiplication

(B.2a)

(B.2b)

• (cf.) For this multiplication to be done, the number of columns of A must equal the number of rows of B.
• (cf.) Note that 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)

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 c_kn = (−1)^k+nM_kn is called the cofactor of a_kn.

Especially, the determinants of a 2 × 2 matrix A_2×2 and a 3 × 3 matrix A_3×3 are

(B.4a)

(B.4b)