Nguồn ngoài
Matrix Analysis
Equilibria and the solution of linear and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration.
- Tác giả
- Steve Cox
- Nhà xuất bản
- Rice University
- Nguồn
- LibreTexts
- Giấy phép
- CC BY
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 57 mục
- 01: Matrix Methods for Electrical Systems
- 1.01: Nerve Fibers and the Strang Quartet
- 1.02: Chapter 1 Exercises
- 02: Matrix Methods for Mechanical Systems
- 2.01: A Uniaxial Truss
- 2.02: A Small Planar Truss
- 2.03: The General Planar Truss
- 2.04: Chapter 2 Exercises
- 03: The Fundamental Subspaces
- 3.01: Column Space
- 3.02: Null Space
- 3.03: The Null and Column Spaces- An Example
- 3.04: Left Null Space
- 3.05: Row Space
- 3.06: Exercises- Columns and Null Spaces
- 3.07: Supplements - Vector Space
- 3.08: Supplements - Subspaces
- 3.09: Supplements - Row Reduced Form
- 04: Least Squares
- 4.01: Least Squares
- 05: Matrix Methods for Dynamical Systems
- 5.01: Nerve Fibers and the Dynamic Strang Quartet
- 5.02: The Laplace Transform
- 5.03: The Inverse Laplace Transform
- 5.04: The Backward-Euler Method
- 5.05: Exercises- Matrix Methods for Dynamical Systems
- 5.06: Supplemental - Matrix Analysis of the Branched Dendrite Nerve Fiber
- 06: Complex Analysis I
- 6.01: Complex Numbers Vectors and Matrices
- 6.02: Complex Functions
- 6.03: Complex Differentiation
- 6.04: Exercises- Complex Numbers Vectors and Functions
- 07: Complex Analysis II
- 7.01: Cauchy's Theorem
- 7.02: Cauchy's Integral Formula
- 7.03: The Inverse Laplace Transform- Complex Integration
- 7.04: Exercises- Complex Integration
- 08: The Eigenvalue Problem
- 8.01: Introduction to the Eigenvalue Problem
- 8.02: The Resolvent
- 8.03: The Partial Fraction Expansion of the Resolvent
- 8.04: The Spectral Representation
- 8.05: The Eigenvalue Problem- Examples
- 8.06: The Eigenvalue Problem- Exercises
- 09: The Symmetric Eigenvalue Problem
- 9.01: The Spectral Representation of a Symmetric Matrix
- 9.02: Gram-Schmidt Orthogonalization
- 9.03: The Diagonalization of a Symmetric Matrix
- 10: The Matrix Exponential
- 10.01: Overview
- 10.02: The Matrix Exponential as a Limit of Powers
- 10.03: The Matrix Exponential as a Sum of Powers
- 10.04: The Matrix Exponential via the Laplace Transform
- 10.05: The Matrix Exponential via Eigenvalues and Eigenvectors
- 10.06: The Mass-Spring-Damper System
- 11: Singular Value Decomposition
- 11.01: The Singular Value Decomposition