A Bridge to Linear Algebra / Dragu Atanasiu & Piotr Mikusinski.
Material type: TextLanguage: English Publication details: Singapore : World Scientific Publishing Co Pte Ltd, 2020.Description: xi, 494 pages : 25 cmISBN:- 9780000988478
- 23 512.5 ATA
Item type | Current library | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|
General Books | CUTN Central Library Sciences | Non-fiction | 512.5 ATA (Browse shelf(Opens below)) | Available | 48027 |
TABLE OF CONTENTS
1. Basic ideas of linear algebra
2. Matrices
3. The vector space R2
4. The vector space R3
5. Determinants and bases in R3
6. Singular value decomposition of 3 x 2 matrices
7. Diagonalization of 3 x 3 matrices
8. Applications to geometry
9. Rotations
10. Problems in plane geometry
Intro; Contents; Preface; 1 Basic ideas of linear algebra; 1.1 2 x 2 matrices; 1.2 Inverse matrices; 1.3 Determinants; 1.4 Diagonalization of 2 x 2 matrices; 2 Matrices; 2.1 General matrices; 2.2 Gaussian elimination; 2.3 The inverse of a matrix; 3 The vector space R2; 3.1 Vectors in R2; 3.2 The dot product and the projection on a vector line in R2; 3.3 Symmetric 2 x 2 matrices; 4 The vector space R3; 4.1 Vectors in R3; 4.2 Projections in R3; 5 Determinants and bases in R3; 5.1 The cross product; 5.2 Calculating inverses and determinants of 3 x 3 matrices 5.3 Linear dependence of three vectors in R35.4 The dimension of a vector subspace of R3; 6 Singular value decomposition of 3 x 2 matrices; 7 Diagonalization of 3£3 matrices; 7.1 Eigenvalues and eigenvectors of 3 x 3 matrices; 7.2 Symmetric 3 x 3 matrices; 8 Applications to geometry; 8.1 Lines in R2; 8.2 Lines and planes in R3; 9 Rotations; 9.1 Rotations in R2; 9.2 Quadratic forms; 9.3 Rotations in R3; 9.4 Cross product and the right-hand rule; 10 Problems in plane geometry; 10.1 Lines and circles; 10.2 Triangles; 10.3 Geometry and trigonometry 10.4 Geometry problems fromthe International Mathematical Olympiads11 Problems for a computer algebra system; 12 Answers to selected exercises; Bibliography; Index
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