Finite Dimensional Vector Spaces Linear Vector Spaces Spectral

Finite Dimensional Vector Spaces • • • Linear Vector Spaces Spectral Theory for Matrices Geometrical Significance of Eigenvalues Fredholm Alternative Theorem Least Squares Solutions – Pseudo Inverses Generalized Pencil-of-Function Method R. B. Wu

Linear Vector Spaces R. B. Wu

Bases R. B. Wu

Inner Product R. B. Wu

Generalized Magnitude & Direction R. B. Wu

Gram-Schmidt Orthogonalization R. B. Wu

Coordinate Transformation R. B. Wu

Eigenpairs R. B. Wu

Invariant Manifold R. B. Wu

Invariant Manifold (cont’) R. B. Wu

Spectral Decomposition Theorem R. B. Wu

Graphic Explanation R. B. Wu

Maximum Principle R. B. Wu

Courant Minimax Principle R. B. Wu

Applications of Sturm Sequence R. B. Wu

Fredholm Alternative Theorem R. B. Wu

Fredholm Alternative Theorem (cont’) R. B. Wu

Least Squares Solutions R. B. Wu

Least Squares Pseudo Inverse R. B. Wu

Pseudo Inverse (cont’) R. B. Wu

Singular Value Decomposition R. B. Wu

Singular Value Decomposition (cont’) R. B. Wu

Singular Value Decomposition (cont’) R. B. Wu

Singular Value Decomposition (cont’) R. B. Wu

Generalized Pencil-of-function Method R. B. Wu

Generalized Pencil-of-function Method (cont’) R. B. Wu

Extraction of Modal Coefficients R. B. Wu

Choice of Parameter L R. B. Wu

Numerical Results 2 m load I(t) Einc(t) Gaussian pulse N=114 By GPOF (L = N/2 = 57) d = 9. 3, 7. 7, 0. 45, 0. 42, 0. 057, 0. 056, 0. 039, 0. 0388, 0. 0052, . . z = -0. 0204 j 0. 281, -0. 0266 j 0. 642, -0. 0046 j 1. 17, 0. 0039 j 1. 27(? ) b = 0. 3835, 0. 02456, 0. 0009379, 0. 0007506 f = 0. 0694, 0. 204, 0. 372, 0. 404(? ) GHz f = 0. 0684, 0. 203, 0. 391, 0. 414 GHz R. B. Wu