MATH1002 Lecture 12: Diagonalisation, more on applications
24 Jul 2018
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Document Summary
D is diagonal if all entries off tneaiagong. Note that eigenvalues of a diagonal matrix are entries on the diagonal. Matrix invertible if there is such that a diagonal. P det are (a) such det that ( pdp in dltl d) the definition out (d) dltfp ) mm above then det ( pt ) mm. D is invertible all diagonal entries are non zero (b) X ) the same matrix diagonal ( dnn - 7) eigenvalues d. , Api =dup~ , columns are ttpn equal tdnnpn. This with each means to , a. corresponding pj. In eigenvalues n } is nonzero eigenvectors of. X of of x geometric multiplicity algebraic multiplicity. Pdp case where lin . indep . eigenvectors , diagonal elements are. D is the whose matrix the diagonal columns matrix corresponding eigenvalues , i. e. d= = xjxj for each je { 1 n } themark of. 1 then so is its the algebraic multiplicity.
