Algebra A Text-Book Of DeterminantsPDF电子书下载

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PART Ⅰ DETERMINANTS 1

PRELIMINARY NOTE：NUMBER，NUMBER FIELDS，AND MATRICES 1

Ⅰ．ELEMENTARY PROPERTIES OF DETERMINANTS 5

Ⅱ．THE MINORS OF A DETERMINANT 28

Ⅲ．THE PRODUCT OF TWO DETERMINANTS 41

Ⅳ．JACOBI＇S THEOREM AND ITS EXTENSIONS 55

Ⅴ．SYMMETRICAL AND SKEW-SYMMETRICAL DETERMINANTS 59

PART Ⅱ MATRICES 65

Ⅵ．DEFINITIONS AND ELEMENTARY PROPERTIES 67

Ⅶ．RELATED MATRICES 83

Ⅷ．THE RANK OF A MATRIX 93

Ⅸ．DETERMINANTS ASSOCIATED WITH MATRICES 109

PART Ⅲ LINEAR AND QUADRATIC FORMS 117

Ⅹ．ALGEBRAIC FORMS：LINEAR TRANSFORMATIONS 119

Ⅺ．THE POSITIVE-DEFINITE FORM 135

Ⅻ．THE CHARACTERISTIC EQUATION AND CANONICAL FORMS 144

ⅩⅢ．ORTHOGONAL TRANSFORMATIONS 160

ⅩⅣ．INVARIANTS AND COVARIANTS 169

ⅩⅤ．LATENT VECTORS 200

INDEX 219

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