Page 434 - 35Linear Algebra

434 INDEX

concept of, 117 homogeneous equation, 67
notion of, 195 Homogeneous solution
Dimension formula, 295 an example, 67
Direct sum, 268 Homomorphism, 111
Domain, 34, 289 Hyperplane, 65, 86
Dot product, 89
Dual vector space, 359 Identity matrix, 139
2 × 2, 41
Dyad, 255
Inner product, 91, 254
Eigenspace, 237 Invariant direction, 229
Eigenvalue, 230, 233 Inverse Matrix, 55
multiplicity of, 234 Invertible, 150
Eigenvector, 230, 233 invertiblech3, 55
Einstein, Albert, 68 Involution, 134, 272
Elementary matrix, 174
Jordan cell, 250, 411
swapping rows, 175
Elite NASA engineers, 344 Kernel, 292
Equivalence relation, 250 Kindergarten, 90
EROs, 42 Kirchoff’s laws, 342
Euclidean length, 88 Kronecker delta, 254
Even permutation, 171
Expansion by minors, 186 Law of Cosines, 88
Least squares, 303
Fibonacci numbers, 364 solutions, 304
Field, 317 Left singular vectors, 311
Forward substitution, 160 Length of a vector, 90
free variables, 46 Linear combination, 20, 205, 237
Fundamental theorem of algebra, 234 Linear dependence theorem, 205
Fundamental Theorem of Linear Al- Linear independence
gebra, 299 concept of, 195
Linear Map, 111
Galois, 108 Linear Operator, 111
Gaussian elimination, 39 linear programming, 71
Golden ratio, 349 Linear System
Goofing up, 153 concept of, 21
Gram–Schmidt orthogonalization pro- Linear Transformation, 111
cedure, 264 concept of, 23
Graph theory, 135 Linearly dependent, 204

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