Linear Algebra 3 - Exam 2

positive operator

square root

characterization of positive operators

uniqueness of square roots

isometry

characterization of isometries

description of isometries when F = C

polar decomposition

singular values

singular value decomp

finding sing val’s w/o square roots

sequence of increasing null spaces

equality in the sequence of null spaces

null spaces stop growing

V direct sum

generalized eigenvector

generalized eigenspace

description of gen e-spaces

lin. ind. gen e-vecs

nilpotent

nilpotent op raised to dimV

matrix of nilpotent operator

null(pT) & ran(pT) invariant

operators on complex v.s.’s

basis of gen e-vecs

multiplicity

sum of mult’s

block diag matrix

block diag matrix w/ u.t. blocks

identity plus nilpotent

review the HW prob for this one

invertible operators over C have ______

characteristic polynomial

degrees and zeros of char poly

cayley-hamilton theorem

monic poly

minimal polynomial

q(T) = 0

char poly w/r/t min poly

zeros of the min poly

basis corr to a nilpotent operator

Jordan basis

Jordan form