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from Dr. R. Kochendörfer's "Determinants and Matrices", published by Teubner in Leipzig in 1961.

Contents

I. Preliminaries	18. Contragredient and orthogonal matrices	VIII. More about determinants and matrices
1. Sum/product symbols	V. Vector spaces. Rank of a matrix	35. Vandermonde determinants
2. Mathematical induction	19. Vector spaces	36. Hadamard's determinant estimate
3. Polynomials	20. Linear dependence	37. Laplace's expansion rule
4. Permutations	21. Relationship between different bases	38. Partial matrices
II. Determinants	22. Dimensions of partial spaces	39. Characteristic roots
5. Determinants of second and third order	23. Rank of matrix	40. Kronecker product
6. Determinants of order n	24. Rank of a product	41. Cayley-Hamilton relations
III. The most important properties of Determinants	25. Orthogonal bases	X. Similarity
7. Determinants, most important properties	VI Linear Spaces	^{42. Classes of}I^similarity
8. Description of determinants according to Weierstrass	26. Homogeneous/ non-homogeneous equations	43. Linear mapping
9. Determinant of transposed matrix	27. General solution of homogeneous system	44. Decomposition into components with a single characteristic root.
10. Expansion formulae	28. Solubility of non-homogeneous systems of equations	45. Decomposition into elementary components
11. Evaluation of determinants	29. Homogeneous variable	46. Jordan's normal form
12. Cramer's Rule	30. Numerical solution of linear equations	47. Similarity to diagonal matrices
13. Multiplication of determinants	VII Hermitian/Quadratic forms
IV. Matrices	31. Transformation of Hermitian forms
14. Multiplication of matrices	32. Characteristic roots. Eigen vectors.
15. Inverse Matrix	33. Principal axes transformation
16. Group of regular matrices	34. Definite Hermitian form
17. Addition of matrices

Index