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