Sharedsage_worksheets / ADS_matrix.ipynbOpen in CoCalc
Author: Ken Levasseur
Description: Worksheets related to Applied Discrete Structures

Row Reduction

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C = Matrix(QQ,[[1,1,1,1],[5,1,2,2]]);C print '--------------------' C.echelon_form()
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[ 1 0 1/4 1/4] [ 0 1 3/4 3/4]
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H=Matrix(Integers(2),[[1,1,0,0,1,1],[1,0,1,0,1,0],[1,0,1,1,0,1],[0,1,1,1,0,0]]);H print '--------------------' H.echelon_form()
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H=Matrix(Integers(2),[[1,1,0,1,0,0,1],[1,0,1,0,1,0,0],[0,1,1,0,0,1,0]]);H print '*****************' H.echelon_form()
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H2=Matrix(Integers(2),[[1,1,0,1,1,1],[1,0,1,1,0,0],[0,1,1,0,1,0]]);H2 print '*****************' H2.echelon_form()
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A=[[2,1,0,4],[-1,2,1,0],[0,-1,2,1]] A
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matrix(A)
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var (' D, P') A = Matrix (QQ, [[4, 1, 0], [1, 5, 1], [0, 1, 4]]);A
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(D,P)=A.right_eigenmatrix();(D,P)
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P.inverse()*A*P
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A2=Matrix(QQ,[[8,1,0],[1,5,1],[0,1,7]])
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P=A2.right_eigenmatrix()[1] P.numerical_approx(digits=3) print '------------------' D=(P.inverse()*A2*P);D.numerical_approx(digits=3)
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A=Matrix(QQ,[[1, 0, 0],[0,2,1],[1,-1,4]]) A.right_eigenmatrix()
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A=Matrix(QQ,[[2,1],[2,3]]) A.exp()
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Matrix?
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