Page 435 - 35Linear Algebra

INDEX 435

Linearly independent, 204 Permutation, 170
lower triangular, 58 Permutation matrices, 249
Lower triangular matrix, 159 “Perp”, 270
Lower unit triangular matrix, 162 Pivot variables, 46
LU decomposition, 159 Pre-image, 288
Projection, 239
Magnitude, see also Length of a vec-
tor QR decomposition, 265
Matrix, 133 Queen Quandary, 348
diagonal of, 138
Random, 301
entries of, 134
Rank, 295
Matrix equation, 25
column rank, 297
Matrix exponential, 144
row rank, 297
Matrix multiplication, 25, 33
Recursion relation, 349
Matrix of a linear transformation, 218
Reduced row echelon form, 43
Minimal spanning set, 209
Right singular vector, 310
Minor, 186
Row echelon form, 50
Multiplicative function, 186
Row Space, 138
Newton’s Principiæ, 346 Row vector, 134
Non-invertible, 150
Scalar multiplication
Non-pivot variables, 46
n-vectors, 84
Nonsingular, 150
Sign function, 171
Norm, see also Length of a vector
Similar matrices, 247
Nullity, 295
singular, 150
Odd permutation, 171 Singular values, 284
Orthogonal, 90, 254 Skew-symmetric matrix, see Anti-symmetric
Orthogonal basis, 255 matrix
Orthogonal complement, 269 Solution set, 65
Orthogonal decomposition, 262 set notation, 66
Orthogonal matrix, 260 Span, 198
Orthonormal basis, 255 Square matrices, 143
Outer product, 254 Square matrix, 138
Standard basis, 217, 220
2
Parallelepiped, 192 for R , 122
Particular solution Subspace, 195
an example, 67 notion of, 195
Pauli Matrices, 126 Subspace theorem, 196

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