From the reviews: "Shafarevich (Russian Academy of Sciences) and Remizov (Ecole Polytechnique, CNRS, France) provide insightful comments that apply not only to linear algebra but also to mathematics in general. ... The book is quite readable ... . Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, and professionals." (J. R. Burke, Choice, Vol. 50 (8), April, 2013) "This beautiful textbook not only reflects I. R. Shafarevich's unrivalled mastery of mathematical teaching and expository writing, but also the didactic principles of the Russian mathematical school in teaching basic courses such as linear algebra and analytic geometry. ... made accessible to a wide audience of international readers, and to further generations of students, too. ... this book may be regarded as a historical document in the relevant textbook literature ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1256, 2013)

• Preface.- Preliminaries.- 1. Linear Equations.- 2. Matrices and Determinants.- 3. Vector Spaces.- 4. Linear Transformations of a Vector Space to Itself.- 5. Jordan Normal Form.- 6. Quadratic and Bilinear Forms.- 7. Euclidean Spaces.- 8. Affine Spaces.- 9. Projective Spaces.- 10. The Exterior Product and Exterior Algebras.- 11. Quadrics.- 12. Hyperbolic Geometry.- 13. Groups, Rings, and Modules.- 14. Elements of Representation Theory.- Historical Note.- References.- Index

From the reviews: "Shafarevich (Russian Academy of Sciences) and Remizov (Ecole Polytechnique, CNRS, France) provide insightful comments that apply not only to linear algebra but also to mathematics in general. ... The book is quite readable ... . Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, and professionals." (J. R. Burke, Choice, Vol. 50 (8), April, 2013) "This beautiful textbook not only reflects I. R. Shafarevich's unrivalled mastery of mathematical teaching and expository writing, but also the didactic principles of the Russian mathematical school in teaching basic courses such as linear algebra and analytic geometry. ... made accessible to a wide audience of international readers, and to further generations of students, too. ... this book may be regarded as a historical document in the relevant textbook literature ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1256, 2013)

• Preface.- Preliminaries.- 1. Linear Equations.- 2. Matrices and Determinants.- 3. Vector Spaces.- 4. Linear Transformations of a Vector Space to Itself.- 5. Jordan Normal Form.- 6. Quadratic and Bilinear Forms.- 7. Euclidean Spaces.- 8. Affine Spaces.- 9. Projective Spaces.- 10. The Exterior Product and Exterior Algebras.- 11. Quadrics.- 12. Hyperbolic Geometry.- 13. Groups, Rings, and Modules.- 14. Elements of Representation Theory.- Historical Note.- References.- Index

From the reviews: "Shafarevich (Russian Academy of Sciences) and Remizov (Ecole Polytechnique, CNRS, France) provide insightful comments that apply not only to linear algebra but also to mathematics in general. ... The book is quite readable ... . Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, and professionals." (J. R. Burke, Choice, Vol. 50 (8), April, 2013) "This beautiful textbook not only reflects I. R. Shafarevich's unrivalled mastery of mathematical teaching and expository writing, but also the didactic principles of the Russian mathematical school in teaching basic courses such as linear algebra and analytic geometry. ... made accessible to a wide audience of international readers, and to further generations of students, too. ... this book may be regarded as a historical document in the relevant textbook literature ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1256, 2013)

• Preface.- Preliminaries.- 1. Linear Equations.- 2. Matrices and Determinants.- 3. Vector Spaces.- 4. Linear Transformations of a Vector Space to Itself.- 5. Jordan Normal Form.- 6. Quadratic and Bilinear Forms.- 7. Euclidean Spaces.- 8. Affine Spaces.- 9. Projective Spaces.- 10. The Exterior Product and Exterior Algebras.- 11. Quadrics.- 12. Hyperbolic Geometry.- 13. Groups, Rings, and Modules.- 14. Elements of Representation Theory.- Historical Note.- References.- Index