MATLAB Matrix Algebra (Matlab Solutions)

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java.

MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and how to solve systems of linear equations are described, with numerous examples. A section is dedicated to sparse matrices and other types of special matrices. In addition to its treatment of matrices, you will also learn how MATLAB can be used to work with arrays, lists, tables, sequences and sets.

What you’ll learn

• How to use MATLAB to work with numeric and symbolic variables, including vector and matrix variables.

• How MATLAB supports functions with vectors and matrices as arguments.

• Applications such as change of bases, classification of quadratic forms and solutions of systems of linear equations.

• How to find various matrix decompositions using MATLAB.

• How to work with sparse matrices and other special matrices.

• How to manipulate arrays, lists, tables, sequences and sets.

• How to use MATLAB to work with matrix algebra over the complex field.

Who this book is for

This book is for anyone who wants to work on matrix algebra problems in a practical, hands-on manner using MATLAB. You'll already have a core understanding of undergraduate level linear algebra, and have access to an installed version of MATLAB, but no previous experience of MATLAB is assumed.

Table of Contents

1. Introducing MATLAB for Matrix and Vector Variables

2. MATLAB and Matrix Algebra

3. Sequences, Arrays, Tables, Lists and Sets

4. Vector Spaces and Linear Applications with MATLAB

5. MATLAB for Vector and Matrix Functions of Complex Variables

MATLAB 是一種高階語言和環境，用於數值計算、可視化和編程。使用 MATLAB，您可以分析數據、開發算法，並創建模型和應用程序。語言、工具和內置的數學函數使您能夠探索多種方法，並比使用電子表格或傳統編程語言（如 C/C++ 或 Java）更快地找到解決方案。

《MATLAB 矩陣代數》通過實際的實踐指導和結果，介紹了 MATLAB 語言，讓您能夠快速實現目標。從符號和數值變量開始，重點是向量和矩陣變量，然後您將繼續檢查支持向量和矩陣作為參數的函數和操作，包括基於分析父函數的函數。詳細介紹了尋找矩陣的特徵值和特徵向量的計算方法，從而得到各種矩陣分解。描述了基於基底變換、二次型的分類以及如何解決線性方程組等應用，並提供了大量示例。還專門介紹了稀疏矩陣和其他類型的特殊矩陣。除了處理矩陣外，您還將學習如何使用 MATLAB 處理數組、列表、表格、序列和集合。

您將學到什麼：
• 如何使用 MATLAB 處理數值和符號變量，包括向量和矩陣變量。
• MATLAB 如何支持帶有向量和矩陣作為參數的函數。
• 基於 MATLAB 的應用，如基底變換、二次型的分類和線性方程組的解。
• 如何使用 MATLAB 找到各種矩陣分解。
• 如何處理稀疏矩陣和其他特殊矩陣。
• 如何操作數組、列表、表格、序列和集合。
• 如何使用 MATLAB 在複數域上進行矩陣代數。

這本書適合對矩陣代數問題有實際、實踐性需求的任何人使用 MATLAB。您應該已經具備本科線性代數的核心理解，並且可以使用已安裝的 MATLAB 版本，但不需要有 MATLAB 的先前經驗。

目錄：
1. 介紹 MATLAB 的矩陣和向量變量
2. MATLAB 和矩陣代數
3. 序列、數組、表格、列表和集合
4. 向量空間和使用 MATLAB 的線性應用
5. MATLAB 用於複變數的向量和矩陣函數