forked from APEXCalculus/Fundamentals-of-Matrix-Algebra
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathFundamentals_of_Matrix_Algebra_3rd_Ed.idx
130 lines (130 loc) · 6.25 KB
/
Fundamentals_of_Matrix_Algebra_3rd_Ed.idx
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
\indexentry{linear equation|hyperpage}{3}
\indexentry{system of linear equations!definition|hyperpage}{3}
\indexentry{system of linear equations!solution|hyperpage}{3}
\indexentry{solution|hyperpage}{3}
\indexentry{matrix!definition|hyperpage}{7}
\indexentry{augmented matrix|hyperpage}{8}
\indexentry{matrix!augmented|hyperpage}{8}
\indexentry{elementary row operations|hyperpage}{13}
\indexentry{reduced echelon form|hyperpage}{14}
\indexentry{leading one|hyperpage}{14}
\indexentry{reduced row echelon form|hyperpage}{14}
\indexentry{row echelon form|hyperpage}{14}
\indexentry{Gaussian elimination|hyperpage}{15}
\indexentry{Gaussian elimination!forward steps|hyperpage}{17}
\indexentry{Gaussian elimination!backward steps|hyperpage}{17}
\indexentry{Gaussian elimination|hyperpage}{18}
\indexentry{solution!types|hyperpage}{24}
\indexentry{solution!unique|hyperpage}{24}
\indexentry{solution!infinite|hyperpage}{24}
\indexentry{solution!none|hyperpage}{24}
\indexentry{system of linear equations!consistent|hyperpage}{24}
\indexentry{system of linear equations!inconsistent|hyperpage}{24}
\indexentry{consistent|hyperpage}{24}
\indexentry{inconsistent|hyperpage}{24}
\indexentry{free variable|hyperpage}{25}
\indexentry{variable!free|hyperpage}{25}
\indexentry{variable!dependent|hyperpage}{27}
\indexentry{variable!basic|hyperpage}{27}
\indexentry{basic variable|hyperpage}{27}
\indexentry{variable!independent|hyperpage}{27}
\indexentry{variable!free|hyperpage}{27}
\indexentry{free variable|hyperpage}{27}
\indexentry{system of linear equations!consistent|hyperpage}{27}
\indexentry{leading one|hyperpage}{27}
\indexentry{solution!infinite|hyperpage}{27}
\indexentry{system of linear equations!consistent|hyperpage}{27}
\indexentry{leading one|hyperpage}{27}
\indexentry{solution!infinite|hyperpage}{27}
\indexentry{system of linear equations!inconsistent|hyperpage}{29}
\indexentry{leading one|hyperpage}{29}
\indexentry{particular solution|hyperpage}{30}
\indexentry{solution!particular|hyperpage}{30}
\indexentry{problem solving|hyperpage}{37}
\indexentry{matrix!equality|hyperpage}{46}
\indexentry{matrix!addition|hyperpage}{47}
\indexentry{matrix!scalar multiplication|hyperpage}{47}
\indexentry{zero matrix|hyperpage}{49}
\indexentry{matrix!the zero matrix|hyperpage}{49}
\indexentry{matrix!arithmetic properties|hyperpage}{49}
\indexentry{vector!column|hyperpage}{52}
\indexentry{vector!row|hyperpage}{52}
\indexentry{matrix!multiplication|hyperpage}{54}
\indexentry{identity matrix|hyperpage}{61}
\indexentry{matrix!identity matrix|hyperpage}{61}
\indexentry{matrix!multiplication!properties|hyperpage}{62}
\indexentry{Parallelogram Law|hyperpage}{69}
\indexentry{vector!length|hyperpage}{74}
\indexentry{system of linear equations!homogeneous|hyperpage}{87}
\indexentry{homogeneous|hyperpage}{87}
\indexentry{consistent|hyperpage}{88}
\indexentry{system of linear equations!consistent|hyperpage}{88}
\indexentry{homogeneous|hyperpage}{88}
\indexentry{homogeneous|hyperpage}{90}
\indexentry{consistent|hyperpage}{90}
\indexentry{system of linear equations!consistent|hyperpage}{90}
\indexentry{solution!unique|hyperpage}{90}
\indexentry{solution!infinite|hyperpage}{90}
\indexentry{inverse!uniqueness|hyperpage}{106}
\indexentry{matrix!inverse|hyperpage}{106}
\indexentry{inverse!definition|hyperpage}{106}
\indexentry{inverse!computing|hyperpage}{107}
\indexentry{matrix!inverse|hyperpage}{107}
\indexentry{solution!unique|hyperpage}{110}
\indexentry{Invertible Matrix Theorem|hyperpage}{113}
\indexentry{inverse!properties|hyperpage}{113}
\indexentry{inverse!Invertible Matrix Theorem|hyperpage}{113}
\indexentry{diagonal|hyperpage}{118}
\indexentry{inverse!properties|hyperpage}{119}
\indexentry{transpose|hyperpage}{121}
\indexentry{transpose!definition|hyperpage}{122}
\indexentry{matrix!transpose|hyperpage}{122}
\indexentry{transpose!definition|hyperpage}{122}
\indexentry{diagonal!definition|hyperpage}{123}
\indexentry{triangular matrix!definition|hyperpage}{123}
\indexentry{matrix!diagonal|hyperpage}{123}
\indexentry{matrix!triangular|hyperpage}{123}
\indexentry{transpose!properties|hyperpage}{126}
\indexentry{symmetric|hyperpage}{128}
\indexentry{skew symmetric|hyperpage}{128}
\indexentry{transpose!symmetric|hyperpage}{128}
\indexentry{transpose!skew-symmetric|hyperpage}{128}
\indexentry{symmetric!definition|hyperpage}{128}
\indexentry{skew symmetric!definition|hyperpage}{128}
\indexentry{antisymmetric|hyperpage}{128}
\indexentry{symmetric!theorem|hyperpage}{129}
\indexentry{skew symmetric!theorem|hyperpage}{129}
\indexentry{pseudoinverse|hyperpage}{130}
\indexentry{trace!definition|hyperpage}{131}
\indexentry{trace!properties|hyperpage}{133}
\indexentry{determinant!of $2\times 2$ matrices|hyperpage}{136}
\indexentry{matrix!determinant|hyperpage}{136}
\indexentry{matrix!minor|hyperpage}{137}
\indexentry{matrix!cofactor|hyperpage}{137}
\indexentry{minor|hyperpage}{137}
\indexentry{cofactor|hyperpage}{137}
\indexentry{cofactor!expansion|hyperpage}{139}
\indexentry{matrix!determinant|hyperpage}{141}
\indexentry{determinant!definition|hyperpage}{141}
\indexentry{cofactor!expansion|hyperpage}{146}
\indexentry{determinant!of triangular matrices|hyperpage}{148}
\indexentry{triangular matrix!determinant|hyperpage}{148}
\indexentry{elementary row operations!and determinants|hyperpage}{150}
\indexentry{determinant!and elementary row operations|hyperpage}{150}
\indexentry{determinant!properties|hyperpage}{154}
\indexentry{Invertible Matrix Theorem|hyperpage}{155}
\indexentry{determinant!$3\times 3$ shortcut|hyperpage}{155}
\indexentry{Cramer's Rule|hyperpage}{159}
\indexentry{eigenvalue!definition|hyperpage}{164}
\indexentry{eigenvector!|hyperindexformat{\see{eigenvalue}}}{164}
\indexentry{characteristic polynomial|hyperpage}{168}
\indexentry{eigenvalue!finding|hyperpage}{168}
\indexentry{eigenvalue!properties|hyperpage}{182}
\indexentry{Invertible Matrix Theorem|hyperpage}{183}
\indexentry{linear transformation!definition|hyperpage}{204}
\indexentry{linear transformation!standard matrix of|hyperpage}{207}
\indexentry{linear transformation!and \ensuremath {\mathaccentV {vec}17E{\text {\it 0}}}|hyperpage}{208}
\indexentry{standard unit vector|hyperpage}{208}
\indexentry{linear transformation!standard matrix of|hyperpage}{209}
\indexentry{linear transformation!conditions on|hyperpage}{213}
\indexentry{vector!length|hyperpage}{224}