Linear algebra. Step by step
type: Item
instance of: scholarly article
zbMATH Open document ID: 1334.15003
author: Kuldeep Singh
publication date: 2013-09-05T00:00:00Z
Mathematics Subject Classification ID: 15-01
Mathematics Subject Classification ID: 00A05
Mathematics Subject Classification ID: 00A06
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 6206220
zbMATH Keywords: textbook
zbMATH Keywords: linear equations
zbMATH Keywords: Euclidean space
zbMATH Keywords: vector space
zbMATH Keywords: inner product space
zbMATH Keywords: linear transformation
zbMATH Keywords: determinant
zbMATH Keywords: inverse matrix
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
MaRDI profile type: Publication
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title: Linear algebra. Step by step
review text: Linear algebra plays an important role in many fields where students are not normally strong in mathematics. The author has written this text with these students in mind. To this end he has incorporated a large number of examples and step-by-step explanations of every new concept and result, as well as many numerical and also theoretical exercises with solutions at the back of the book or available online. The students are thus led by the hand and spoon-fed all the way which in the reviewer's opinion makes the book not very suitable for mathematics students. The chapter headings are: 1. Linear equations and matrices, 2. Euclidean space, 3. General vector spaces, 4. Inner product spaces, 5. Linear transformations, 6. Determinants and the inverse matrix, 7. Eigenvalues and eigenvectors. The book is rigorous in the sense that definitions, results and proofs are stated carefully.NEWLINENEWLINEThere are, however, some inconsistencies and shortcomings. Chapter 2 bridges the gap between the vector geometry learnt at school and the concept of an \(n\)-dimensional vector space, while Chapter 3 presents the formal definition of vector spaces. In Chapter 2, the concept of the angle (measured in degrees) between two vectors (two-dimensional) suddenly appears from nowhere and the cosine rule is fished out of trigonometry. This is then generalized to \(n\) dimensions by means of the formula normally derived from the Cauchy-Schwarz inequality, now using radians which remain unexplained, while the Cauchy-Schwarz inequality is then proved using the above-mentioned formula! In Chapter 3, the Cauchy-Schwarz inequality reappears and is now proved in the usual way, while angles make no appearance. The student will no doubt ask why the earlier simple proof does not work here.NEWLINENEWLINEAn important shortcoming is that the scalars are assumed to be real numbers. Complex numbers are nowhere mentioned. In the last chapter, eigenvectors are introduced as those non-zero vectors that are ju…
reviewed by: Rabe von Randow
description: scientific article; zbMATH DE number 6206220