# diagnew - cfw_VERSION 6 0"IBM INTEL NT"6.0 cfw_USTYLETAB...

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{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 1 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 0 3 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 22 "Diagonaliz ing a Matrix" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "This worksheet sh ows how Maple can be used to diagonalize a matrix " }{XPPEDIT 18 0 "A; " "6#%\"AG" }{TEXT -1 9 " that is " }{TEXT 257 8 "complete" }{TEXT -1 136 "; that is, a matrix whose eigenvectors form a basis for the vecto r space. The idea is simply to find the eigenvectors and form a matrix " }{XPPEDIT 18 0 "S;" "6#%\"SG" }{TEXT -1 40 " with the eigenvectors \+ as columns. Then " }{XPPEDIT 18 0 "S^(-1).A.S = D;" "6#/-%\".G6%)%\"SG ,\$\"\"\"!\"\"%\"AGF(%\"DG" }{TEXT -1 51 " will be a diagonal matrix wi th the eigenvalues of " }{XPPEDIT 18 0 "A;" "6#%\"AG" }{TEXT -1 20 " a long the diagonal." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restar t:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "AA:=Matrix([[5,-8],[-2, 10]]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 491 "The eigenvalue and eig envector commands are as follows. Note that the eigenvector command gi ves you the eigenvalues as a list and the eigenvectors in a matrix (as the columns of the matrix). You can peel off this matrix and use it d irectly or form it by taking individual elements. Depending on the pro blem, one way or the other may be better. We will show both. (Also, so metimes the decimal equivalents are more useful than the radical eigen value solutions, so we use \"evalf\" to get these.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Eigenvalues(AA);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "evalf(Eigenvalues(AA));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eigs2:=Eigenvectors(AA);" }}}{EXCHG {PARA 0 ""

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## This note was uploaded on 02/10/2012 for the course MTH 587 taught by Professor Johnopera during the Spring '11 term at Cleveland State.

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diagnew - cfw_VERSION 6 0"IBM INTEL NT"6.0 cfw_USTYLETAB...

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