Linear Algebra – Exercises and Solutions
Authors
Description
This book contains the statements and complete solutions of the exercises proposed in my book “Linear Algebra”.
Each chapter begins with a list of the definitions relating to it, as well as a summary of the main propositions to be used. These definitions and summaries precede the excellent solutions, permeated with fine observations, presented by Professor Ralph Teixeira.
Your work enhances my book, for which I offer my special thanks. – Elon Lages Lima
Target audience
Higher education
Name: Linear Algebra – Exercises and Solutions
Author(s): e Ralph Costa Teixeira
Pages: 484
Publication: IMPA, 2020
ISBN: 978-65-990528-4-2
Edition: 4
Foreword
I Definitions and Statements
1 Vector Spaces
2 Subspaces
3 Bases
4 Linear transformations
5 Product of Linear Transformations
6 Core and Image
7 Direct Sum and Projection
8 The Matrix of a Linear Transformation
9 Disposal
10 Domestic Product
11 The Deputy
12 Invariant subspaces
13 Self-adjoining operators
14 Orthogonal operators
15 Normal Operators – Real Case
16 Pseudo-inverse
17 Matrix Topics
18 Quadratic shapes
19 Determinants
20 The Characteristic Polynomial
21 Complex Vector Spaces
22 Finite Difference Equations
22.1 Linear systems
22.2 Application of the Cayley-Hamilton Theorem
22.3 Second Order Linear Equations (Homogeneous)
22.4 Equations with Constant Second Member
II Solutions
Chapter 1 Solutions
Solutions from Chapter 2
Solutions from Chapter 3
Solutions from Chapter 4
Solutions from Chapter 5
Solutions from Chapter 6
Solutions from Chapter 7
Solutions from Chapter 8
Solutions from Chapter 9
Solutions from Chapter 10
Solutions from Chapter 11
Solutions from Chapter 12
Solutions from Chapter 13
Solutions from Chapter 14
Solutions from Chapter 15
Solutions from Chapter 16
Solutions from Chapter 17
Solutions from Chapter 18
Solutions from Chapter 19
Solutions from Chapter 20
Solutions from Chapter 21
Solutions from Chapter 22
