Nguồn ngoài
Understanding Linear Algebra
This book arises from my belief that linear algebra, as presented in a traditional undergraduate curriculum, has for too long lived in the shadow of calculus. Many mathematics programs currently require their students to complete at least three semesters of calculus, but only one semester of linear algebra, which often has two semesters of calculus as a prerequisite.
- Tác giả
- David Austin
- Nhà xuất bản
- Grand Valley State University
- Nguồn
- LibreTexts
- Giấy phép
- CC BY
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 40 mục
- 01: Systems of equations
- 1.01: What can we expect
- 1.02: Finding solutions to systems of linear equations
- 1.03: Computation with Sage
- 1.04: Pivots and their influence on solution spaces
- 02: Vectors matrices and linear combinations
- 2.01: Vectors and linear combinations
- 2.02: Matrix multiplication and linear combinations
- 2.03: The span of a set of vectors
- 2.04: Linear independence
- 2.05: Matrix transformations
- 2.06: The geometry of matrix transformations
- 03: Invertibility bases and coordinate systems
- 3.01: Invertibility
- 3.02: Bases and coordinate systems
- 3.03: Image Compression
- 3.04: Determinants
- 3.05: Subspaces of Rp
- 04: Eigenvalues and eigenvectors
- 4.01: An introduction to eigenvalues and eigenvectors
- 4.02: Finding eigenvalues and eigenvectors
- 4.03: Diagonalization similarity and powers of a matrix
- 4.04: Dynamical Systems
- 4.05: Markov chains and Google's PageRank algorithm
- 05: Linear algebra and computing
- 5.01: Gaussian elimination revisited
- 5.02: Finding eigenvectors numerically
- 06: Orthogonality and Least Squares
- 6.01: The dot product
- 6.02: Orthogonal complements and the matrix tranpose
- 6.03: Orthogonal bases and projections
- 6.04: Finding Orthogonal Bases
- 6.05: Orthogonal Least Squares
- 07: The Spectral Theorem and singular value decompositions
- 7.01: Symmetric matrices and variance
- 7.02: Quadratic forms
- 7.03: Principal Component Analysis
- 7.04: Singular Value Decompositions
- 7.05: Using Singular Value Decompositions
- New Page