512 INDEX

inverses, 465type, 465

ideal, 67, 169maximal, 169

inconsistent, 44initial value problem

uniqueness, 408inner product, 263inner product space

adjoint operator, 314integers modulo a prime, 28integral

continuous function, 447operator valued function, 407vector valued function, 406

integral domain, 28, 169integrals

iterated, 450interior point, 245intermediate value theorem, 260intersection, 1intervals

notation, 1invariance of domain, 498invariant subspaces

direct sum, block diagonal matrix, 120inverse image, 3inverses and determinants, 180invertible, 81irreducible, 22

relatively prime, 23isomorphism, 152, 211, 459

extensions, 213iterated integrals, 450iterative methods

alternate proof of convergence, 404diagonally dominant, 405proof of convergence, 402

Jacobi method, 402Jordan

separation theorem, 494Jordan canonical form, 144, 162Jordan curve theorem, 496

ker, 62kernel of a product

direct sum decomposition, 126

Kirchoff’s law, 49, 50

Laplace expansion, 178leading entry, 41least squares, 317lim inf, 29

properties, 32lim sup, 29

properties, 32limiit point, 246limit

continuity, 278infinite limits, 276

limit of a function, 276limit of a sequence, 246

well defined, 246limit point, 276limits

combinations of functions, 276existence of limits, 30

limits and continuity, 278Lindeloff property, 252Lindemann Weierstrass theorem, 206Lindemannn Weierstrass theorem, 199linear combination, 53, 176linear independence, 262linear transformation, 62, 101

defined on a basis, 102dimension of vector space, 102kernel, 124matrix, 101

linear transformationsa vector space, 101commuting, 126composition, matrices, 111sum, 101

linearly independent, 53linearly independent set

enlarging to a basis, 262Lipschitz continuous, 255

Markov matrix, 285limit, 288regular, 288steady state, 285, 288

math induction, 6mathematical induction, 6matrices