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Linear Algebra: Step by Step
Linear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics.
For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance.
The strength of the text is in the large number of examples and the step by step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader's confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading players in the field of linear algebra to provide context for the topics covered.
The dynamic and engaging style of the book includes frequent question and answer sections to test the reader's understanding of the methods introduced, rather than requiring rote learning. When first encountered, the subject can appear abstract and students will sometimes struggle to see its relevance; to counter this, the book also contains interviews with key people who use linear algebra in practice, in both professional and academic life. It will appeal to undergraduate students in mathematics, the physical sciences and engineering.
For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance.
The strength of the text is in the large number of examples and the step by step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader's confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading players in the field of linear algebra to provide context for the topics covered.
The dynamic and engaging style of the book includes frequent question and answer sections to test the reader's understanding of the methods introduced, rather than requiring rote learning. When first encountered, the subject can appear abstract and students will sometimes struggle to see its relevance; to counter this, the book also contains interviews with key people who use linear algebra in practice, in both professional and academic life. It will appeal to undergraduate students in mathematics, the physical sciences and engineering.
616 pages, Paperback
First published January 1, 2013
34 people are currently reading
195 people want to read
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Displaying 1 - 5 of 5 reviews
December 12, 2016
Unbelievably patronising in tone.
September 14, 2017
awesome book for explaining linear algebra step by step it can be understood by beginners
what i really liked in this book the way he explain some topics by giving a question on a specific point and the answer of this question
what really surprised me ! the questions are like those who jumped into your mind while reading
what i really liked in this book the way he explain some topics by giving a question on a specific point and the answer of this question
what really surprised me ! the questions are like those who jumped into your mind while reading
November 14, 2025
Excellent Introduction to Linear Algebra (10/10)
This book was easily one of the best math textbooks I have read in my life! Fantastic explanations and lot of examples and diagrams.
Pros:
1. Extremely clear language at a level of beginning undergraduate student.
2. Lot of questions and answers along with proofs
3. A lot of beginner Linear Algebra books omit proofs (like Strang) but this one doesn't shy away from it.
4. Helps build Intuition through diagrams and proofs
5. Solutions available to all the problems (blessing for someone like me who is self studying)
Cons:
1. There is a difficulty spike in the last chapter particularly SVD/Diagonalisation sections
2. Printing in South Asian editions is in Black and White
Overall if you have been out of touch with undergraduate level mathematics for a long time, this book is perfect. It lays out everything very clearly and doesn't assume lot of prior knowledge. Highly recommended.
This book was easily one of the best math textbooks I have read in my life! Fantastic explanations and lot of examples and diagrams.
Pros:
1. Extremely clear language at a level of beginning undergraduate student.
2. Lot of questions and answers along with proofs
3. A lot of beginner Linear Algebra books omit proofs (like Strang) but this one doesn't shy away from it.
4. Helps build Intuition through diagrams and proofs
5. Solutions available to all the problems (blessing for someone like me who is self studying)
Cons:
1. There is a difficulty spike in the last chapter particularly SVD/Diagonalisation sections
2. Printing in South Asian editions is in Black and White
Overall if you have been out of touch with undergraduate level mathematics for a long time, this book is perfect. It lays out everything very clearly and doesn't assume lot of prior knowledge. Highly recommended.
September 4, 2021
Great book. Thorough examples + all solutions can be found online = great for self-studying.
October 4, 2025
Did it's job!
Displaying 1 - 5 of 5 reviews