Complex‐Valued Matrices and Systems
Roger L. Easton · 2010
The two general disjoint subjects - vectors and matrices and complex numbers and functions - united to consider vectors and matrices formed from complex-valued components. The process of matrix-vector multiplication defined for real-valued components is applied without modification to vectors and matrices with complex-valued components. The complex conjugation operation that is an integral part of the definition of the inner product is not explicitly included in the definition of complex matrix-vector multiplication. The most convenient bases consist of mutually orthonormal vectors that establish a Cartesian coordinate system; the fact that the vectors in the basis are orthogonal ensures that any change in the input vector along the direction of a particular basis vector affects only the corresponding projection. Controlled Vocabulary Terms