Elementary Linear Algebra 6e - Larson, Edwards, Falvo - Index

Elementary Linear Algebra 6e - Larson, Edwards, Falvo - Index

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Unformatted text preview: A Abstraction, 191 Addition of matrices, 48 of vectors, 180, 182, 191 Additive identity of a matrix, 62 of a vector, 186, 191 properties of, 182, 185, 186 Additive inverse of a matrix, 62 of a vector, 186, 191 properties of, 182, 185, 186 Adjoining two matrices, 75 Adjoint of a matrix, 158 Age distribution vector, 458 Age transition matrix, 459 Algebra of matrices, 61 Algebraic properties of the cross product, 338 Angle between two vectors, 282, 286, 296 Approximation Fourier, 346, 348 least squares, 342, 345 n th-order Fourier, 347 Area of a triangle in the xy-plane, 164 Associative property of matrix addition, 61 of scalar multiplication, 182, 191 of vector addition, 182, 191 Augmented matrix, 15 Axioms for vector space, 191 B Back-substitution, 6, 19 Bases and linear dependence, 225 Basis, 221 change of, 252 coordinates relative to, 249 orthogonal, 307 orthonormal, 307 standard, 222, 223, 224 tests for, 229 Basis for the row space of a matrix, 234 Bessels Inequality, 353 Block multiply two matrices, 60 C Cancellation properties, 82 Cauchy, Augustin-Louis (17891857), 285 Cauchy-Schwarz Inequality, 285, 299 Cayley-Hamilton Theorem, 175, 433 Change of basis, 252 Characteristic equation of a matrix, 153, 426 Characteristic polynomial of a matrix, 175, 426 Closed economic system, 106 Closure under scalar multiplication, 182, 185, 191 under vector addition, 182, 185, 191 Coded row matrix, 102 Codomain of a mapping function, 361 Coefficient, 2, 55 leading, 2 Coefficient matrix, 15 Cofactor, 124 expansion by, 126 matrix of, 158 sign patterns for, 124 Column matrix, 47 of a matrix, 14 space, 233 subscript, 14 vector, 47, 232 Column-equivalent, 135 Commutative property of matrix addition, 61 of vector addition, 182, 185, 191 Companion matrix, 475 Component of a vector, 180 Composition of linear transformations, 390, 391 Condition for diagonalization, 437 Conditions that yield a zero determinant, 136 Conic, 265, 266, 267 rotation, 269 Consistent system of linear equations, 5 Constant term, 2 Contraction, 408 Coordinate matrix of a vector, 249 Coordinates relative to an orthonormal basis, 310 of a vector relative to a basis, 249 Counterexample, A6 Cramers Rule, 162, 163 Cross product of two vectors, 336 algebraic properties of, 338 geometric properties of, 339 Cryptogram, 102 Cryptography, 102 D Determinant, 122, 123, 125 evaluation by elementary column operations, 136 evaluation by elementary row operations, 134 expansion by cofactors, 126 of an inverse matrix, 146 of an invertible matrix, 145 of a matrix product, 143 properties of, 142 of a scalar multiple of a matrix, 144 of a transpose, 148 of a triangular matrix, 129 of a matrix, 123 zero, 136 Diagonal matrix, 128 Diagonalizable, 435 Diagonalization condition for, 437 problem, 435 sufficient condition for, 442 Difference of two vectors, 181, 184 Differential operator, 370 Dimension of the solution space, 241 of a vector space, 227 Direct sum of subspaces, 276, 323 Directed line segment, 180 Distance between two vectors, 281, 282,...
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Elementary Linear Algebra 6e - Larson, Edwards, Falvo - Index

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