Book:P.M. Cohn/Linear Equations
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P.M. Cohn: Linear Equations
Published $\text {1958}$, Routledge & Kegan Paul
Subject Matter
Contents
- Preface
- Introduction
- chapter
- 1. Vectors
- 1. Notation
- 2. Definition of vectors
- 3. Addition of vectors
- 4. Multiplication by a scalar
- 5. Geometrical interpretation
- 6--7. Linear dependence of vectors
- 8. A basis for the set of $n$-vectors
- 9. The vector space spanned by a finite number of vectors
- Exercises on chapter $I$
- 2. The Solution of a System of Equations: the Regular Case
- 1--2. Regular systems. Notations and statements of results
- 3--4. Elementary operations on systems
- 5--7. Proof of the Main Theorem
- 8--9. Illustrations to the Main Theorem
- 10. The linear dependence of $n + 1$ vectors in $n$ dimensions
- 11. The construction of a basis
- Exercises on chapter $II$
- 3. Matrices
- 1--2. Definition of a matrix
- 3. The effect of matrices on vectors
- 4. Equality of matrices
- 5. Addition of matrices and multiplication by a scalar
- 6. Multiplication of square matrices
- 7. The zero-matrix and the unit-matrix
- 8. Multiplication of matrices of any shape
- 9. The transpose of a matrix
- Exercises on chapter $III$
- 4. The Solution of a System of Equations: the General Case
- 1--2. The general system and the associated homogeneous system
- 3. The inverse of a regular matrix
- 4. Computation of the inverse matrix
- 5. Application to the solution of regular systems
- 6. The rank of a matrix
- 7. The solution of a homogeneous system
- 8. Illustrations
- 9. The solution of general systems
- 10. Illustrations
- 11. Geometrical interpretation
- Exercises on chapter $IV$
- 5. Determinants
- 1. Motivation
- 2. The $\mathcal 2$-dimensional case
- 3. The $\mathcal 3$-dimensional case
- 4. The rule of signs in the $\mathcal 3$-dimensional case
- 5. Permutations
- 6. The Kronecker $\varepsilon$-symbol
- 7. The determinant of an $n \times n$ matrix
- 8. Cofactors and expansions
- 9. Properties of determinants
- 10. An expression for the cofactors
- 11. Evaluation of determinants
- 12. A formula for the inverse matrix
- 13. Cramer's Rule
- 14. The Multiplication Theorem
- 15. A determinantal criterion for the linear dependence of vectors
- 16. A determinantal expression for the rank of a matrix
- Exercises on chapter $V$
- Answers to the exercises
- Index
Cited by
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $7$: Vector Spaces: $\S 32$. Definition of a Vector Space: Example $62$: Footnote
Source work progress
- 1958: P.M. Cohn: Linear Equations ... (next): Introduction