A_Plus_Maple_Handout

A_Plus_Maple_Handout - Eigenvalues and Eigenvectors...

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(1.2.1) O (1.1.1) O Eigenvalues and Eigenvectors Shortest Template The result of 'eigenvectors' has 3 arguments: 1) eigenvalue 2) multiplicity (ie 1 means not repeated whereas 2 means repeated) 3) eigenvector restart: with(linalg): A:=matrix( [[2,-2],[-1,3]] ); eigen:=eigenvectors(A); Warning, the protected names norm and trace have been redefined and unprotected A := 2 K 2 K 13 eigen := 1, 1, 2 1 ,4 , 1 , K 11 2 x 2 restart: with(linalg): A:=matrix( [[2,-2],[-1,3]] ); M:= evalm(-charmat(A,r)); det_M:=-charpoly(A,r); eigen:=eigenvectors(A); `========= 1 =========`; r1:=eigen[1,1]; u1:=<op(eigen[1,3])>; `========= 2 =========`; r2:=eigen[2,1]; u2:=<op(eigen[2,3])>; Warning, the protected names norm and trace have been redefined and unprotected A := 2 K 2 K M := K r C 2 K 2 K 1 K r C 3 det_M := K r 2 C 5 r K 4
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(1.3.1) O eigen := 1, 1, 2 1 ,4 , 1 , K 11 ========= 1 ========= r1 := 1 u1 := 2 1 ========= 2 ========= r2 := 4 u2 := K 1 1 3 x 3 restart: with(linalg): A:=matrix( [[1,2,2],[2,0,3],[2,3,0]] ); M:= evalm(-charmat(A,r)); det_M:=-charpoly(A,r); eigen:=eigenvectors(A); `========= 1 =========`; r1:=eigen[1,1]; u1:=<op(eigen[1,3])>; `========= 2 =========`; r2:=eigen[2,1]; u2:=<op(eigen[2,3])>; `========= 3 =========`; r3:=eigen[3,1]; u3:=<op(eigen[3,3])>; Warning, the protected names norm and trace have been redefined and unprotected A := 122 203 230 M := K r C 12 2 2 K r 3 23 K r det_M := K r 3 C 17 r C r 2 C 15 eigen := K 3, 1, 0 K , K 1, 1, K 211 ,5 , 1 , 111 ========= 1 =========
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O r1 := K 3 u1 := 0 K 1 1 ========= 2 ========= r2 := K 1 u2 := K 2 1 1 ========= 3 ========= r3 := 5 u3 := 1 1 1 Direction Fields Linear Systems restart: with(DEtools): with(linalg): A:=[-1,-1,-2,0]: a:=A[1]: b:=A[2]: c:=A[3]: d:=A[4]: A:=matrix([[a,b],[c,d]]); eigen:=eigenvectors(A); dx:=diff(x(t),t)=a*x(t) + b*y(t): dy:=diff(y(t),t)=c*x(t) + d*y(t): dfieldplot([dx,dy],[x(t),y(t)],t=-2. .2, x=-2. .2, y=-2. .2); Warning, the name adjoint has been redefined Warning, the protected names norm and trace have been redefined and unprotected A := K 1 K 1 K 20
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O eigen := 1, 1, 1 K 2 , K 2, 1, 1 1 x K 2 K 1 0 1 2 y K 2 K 1 1 2 Nonlinear Systems restart:
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with(DEtools): with(linalg): dx:=2*x(t) - 3*y(t)^2; dy:=3*x(t)^2 - 4*y(t); crit_pts:= solve({dx = 0, dy = 0},{x(t), y(t)}); evalf(%); dfieldplot([diff(x(t),t) = dx, diff(y(t),t) = dy],[x(t),y (t)],t=-2. .2, x=-2. .2, y=-2. .2); Warning, the name adjoint has been redefined Warning, the protected names norm and trace have been redefined and unprotected dx := 2 xt K 3
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This note was uploaded on 06/24/2009 for the course MATH 308 taught by Professor Comech during the Spring '08 term at Texas A&M.

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A_Plus_Maple_Handout - Eigenvalues and Eigenvectors...

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