Introduction to Linear Algebra by Strang

[micromass]

• Author: Gilbert Strang
• Title: Introduction to Linear Algebra
• Amazon Link: https://www.amazon.com/dp/0980232716/?tag=pfamazon01-20
• Prerequisities:
• Contents:

Table of Contents:

[LIST]
[*] Introduction to Vectors
[LIST]
[*] Vectors and Linear Combinations
[*] Lengths and Dot Products
[/LIST]
[*] Solving Linear Equations
[LIST]
[*] Vectors and Linear Equations
[*] The idea of Elimination
[*] Elimination Using Matrices
[*] Rules for Matrix Operations
[*] Inverse Matrices
[*] Elimination = Factorization: A=LU
[*] Transposes and Permutations
[/LIST]
[*] Vectors Spaces and Subspaces
[LIST]
[*] Spaces of Vectors
[*] The Nullspace of A: Solving Ax=0
[*] The Rank and the Row Reduced Form
[*] The Complete Solution to Ax=b
[*] Independence, Basis and Dimension
[*] Dimensions of the Four Subspaces
[/LIST]
[*] Orthogonality
[LIST]
[*] Orthogonality of the Four Subspaces
[*] Projections
[*] Least Square Approximations
[*] Orthogonal Bases and Gram-Schmidt
[/LIST]
[*] Determinants
[LIST]
[*] The Properties of Determinants
[*] Permutations and Cofactors
[*] Cramer's Rule, Inverses, and Volumes
[/LIST]
[*] Eigenvalues and Eigenvectors
[LIST]
[*] Introduction to Eigenvalues
[*] Diagonalizing a Matrix
[*] Applications to Differential Equations
[*] Symmetric Matrices
[*] Positive Definite Matrices
[*] Similar Matrices
[*] Singular Value Decomposition (SVD)
[/LIST]
[*] Linear Transformations
[LIST]
[*] The Idea of a Linear Transformation
[*] The Matrix of a Linear Transformation
[*] Change of Basis
[*] Diagonalization and the Pseudoinverse
[/LIST]
[*] Applications
[LIST]
[*] Matrices in Engineering
[*] Graphs and Networks
[*] Markov Matrices and Economic Models
[*] Linear Programming
[*] Fourier Series: Linear Algebra for Functions
[*] Computer Graphics
[/LIST]
[*] Numerical Linear Algebra
[LIST]
[*] Gaussian Elimination in Practice
[*] Norms and Condition Numbers
[*] Iterative Methods for Linear Algebra
[/LIST]
[*] Complex Vectors and Matrices
[LIST]
[*] Complex Numbers
[*] Hermitian and Unitary Matrices
[*] The Fast Fourier Transform
[/LIST]
[*] Solutions to Selected Exercises
[*] A Final Exam
[*] Matrix Factorizations
[*] Conceptual Questions for Review
[*] Glossary: A Dictionary for Linear Algebra
[*] Index
[*] Teaching Codes
[/LIST]

 

[Permanence]

A very rudimentary textbook. I say that with the uttermost respect for the text. This book doesn't pretend to be anything but an introduction, clear from the title. This book is a brilliantly easy introduction for those learning independently. The writing is clear and the worked examples are easy to follow. Strang already offers many free resources, his lectures are available at (web.mit.edu/18.076).

I would recommend this textbook primarily to those interested in the topic, but walking in with a relatively weak background in mathematics. This book is not for those with a strong background in Linear Algebra.

 

[halo31]

I've read through parts of this text. I personally did not like it. It's wordy and lacks examples in some areas but its much better than David's lay book. Though Strang does have his own video series online for linear algebra which are actually pretty good.

 

[Cod]

As an intro text, I'd say its decent if its your first exposure to linear algebra. Like the poster above me stated, there is a lack of examples and a lot of explanation filler. Also, I'd recommend this text for anyone trying to self-study MIT OCW 18.06.

 

[rezeew]

I am very familiar with the importance of linear algebra in various fields of study. Gilbert Strang's "Introduction to Linear Algebra" is a highly recommended book for anyone looking to understand the fundamentals of this crucial subject.

The book covers all the necessary topics in a clear and concise manner, making it accessible to readers with varying levels of mathematical background. The inclusion of numerous examples and exercises allows for hands-on practice and a deeper understanding of the concepts.

One aspect that sets this book apart is its emphasis on the geometric interpretation of linear algebra. This approach not only makes the subject more intuitive, but also highlights the importance of linear algebra in real-world applications.

I appreciate the comprehensive coverage of topics such as eigenvalues and eigenvectors, orthogonality, and linear transformations, which are essential for understanding more advanced concepts in mathematics and other scientific fields.

Moreover, the book also includes a section on numerical linear algebra, which is becoming increasingly important in the age of big data and computational methods.

In addition, the book provides solutions to selected exercises and a glossary, making it a valuable resource for self-study and reference.

Overall, "Introduction to Linear Algebra" by Gilbert Strang is a well-written and comprehensive book that would benefit students, researchers, and professionals in various fields. I highly recommend it to anyone looking to gain a solid understanding of linear algebra.