Linear Algebra

1. Front Matter

   Pages i-x

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2. Basic Theory

   • Peter Petersen

   Pages 1-123

3. Linear Operators

   • Peter Petersen

   Pages 125-226

4. Inner Product Spaces

   • Peter Petersen

   Pages 227-291

5. Linear Operators on Inner Product Spaces

   • Peter Petersen

   Pages 293-370

6. Determinants

   • Peter Petersen

   Pages 371-427

7. Back Matter

   Pages 383-387

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This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra.
 
This book has several distinguishing features that set it apart from other linear algebra texts.  For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader.  Another motivating aspect of the book isthe excellent and engaging exercises that abound in this text.
 
This textbook is written for an upper-division undergraduate course on Linear Algebra.  The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text.

• Gaussian elimination
• Jordan canonical form
• characteristic polynomial
• complex inner products
• dual spaces
• eigenvalues
• linear algebra
• linear differential equations
• linear maps
• linear operators
• minimal polynomial
• spectral theorem
• vector spaces
• matrix theory

From the reviews:

“The discussions and examples are clear, interesting, and appropriately thorough. There are numerous well-chosen exercises to test the readers understanding and, in some cases, to further develop some of the ideas. … a text that should be included in every undergraduate mathematics library. Even a beginning student will be well-rewarded by exploring various topics in this book.” (F. J. Papp, zbMATH, Vol. 1282, 2014)

• Department of Mathematics, University of California, Los Angeles, Los Angeles, USA

  Peter Petersen

Peter Petersen is currently a professor of mathematics at University of California, Los Angeles.

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