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identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(I-R);

Calculate

identfor-mat_trace-matrix-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

Calculate

identfor-mat_trace-matrix-sum-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

sum(sum(strain(u)[i][...

Calculate

identfor-matrix

R:matrix([a11, a12, a...

I:identfor(R);

inverse(I-R);

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(I-R);

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(I-R);

Calculate

identfor-matrix

R:matrix([a11, a12, a...

I:identfor(R);

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(R);

Calculate

identfor-invert-matrix

R:matrix([a11, a12, a...

I:identfor(R);

invert(I-R);

Calculate

identfor-mat_trace-matrix-sum-trace

strain(u) := matrix([...

stress(e) := b*mat_tr...

sum(sum(strain[i][j] ...

Calculate

identfor

Run Example
(%i1)T: matrix([-lambda, lambda], [mu, -mu]);
                             [ - lambda  lambda ]
(%o1)                        [                  ]
                             [    mu      - mu  ]
(%i2) p0: [1, 0];
(%o2)                               [1, 0]
(%i3) A: s*identfor(T) - T;
                           [ lambda + s  - lambda ]
(%o3)                      [                      ]
                           [    - mu      s + mu  ]
(%i4) Ps: p0.invert(A);
      [              s + mu                             lambda               ]
(%o4) [ ---------------------------------  --------------------------------- ]
      [ (s + mu) (lambda + s) - mu lambda  (s + mu) (lambda + s) - mu lambda ]
(%i5) Pf: partfrac(Ps, s);
               [             lambda                      mu        ]
(%o5)  Col 1 = [ ------------------------------- + --------------- ]
               [ (lambda + mu) (lambda + s + mu)   s (lambda + mu) ]
                          [     lambda                    lambda              ]
                  Col 2 = [ --------------- - ------------------------------- ]
                          [ s (lambda + mu)   (lambda + mu) (lambda + s + mu) ]
(%i6) p0t: ilt(Pf[1,1], s, t);
                            - t (lambda + mu)
                   lambda %e                        mu
(%o6)              -------------------------- + -----------
                          lambda + mu           lambda + mu
(%i7) p1t: ilt(Pf[1,2], s, t);
                                          - t (lambda + mu)
                     lambda      lambda %e
(%o7)              ----------- - --------------------------
                   lambda + mu          lambda + mu
(%i8) declare(lambda, [constant, real, scalar]);
(%o8)                                done
(%i9) assume(lambda >
 0, lambda <
= 1);
(%o9)                    [0 < lambda, lambda - 1 <= 0]
(%i10) declare(mu, [constant, real, scalar]);
(%o10)                               done
(%i11) assume(mu >
 0, mu <
= 1);
(%o11)                       [0 < mu, mu - 1 <= 0]
(%i12) p0SS: limit(p0t, t, inf);
                                      mu
(%o12)                            -----------
                                  lambda + mu
(%i13) p0SS, lambda=1, mu=1, numer;
(%o13)                                0.5
(%i14) p1SS: limit(p1t, t, inf);
                                    lambda
(%o14)                            -----------
                                  lambda + mu
(%i15) p1SS, lambda=1, mu=1, numer;
(%o15)                                0.5
(%i16) for irow: 1 thru length(T) do (T[irow][length(T)]: 1);
(%o16)                               done
(%i17) b: zeromatrix (1, length(T));
(%o17)                             [ 0  0 ]
(%i18) b[1, length(T)]: 1;
(%o18)                                 1
(%i19) pSS: b.invert(T);
                     [        mu             lambda     ]
(%o19)               [ - -------------  - ------------- ]
                     [   - lambda - mu    - lambda - mu ]
(%i20) ratsimp(pSS);
                         [     mu         lambda    ]
(%o20)                   [ -----------  ----------- ]
                         [ lambda + mu  lambda + mu ]
(%i21) 
Run Example
T: matrix([-lambda, lambda], [mu, -mu]);
                             [ - lambda  lambda ]
(%o1)                        [                  ]
                             [    mu      - mu  ]
(%i2) determinant(T);
(%o2)                                  0
(%i3) %%linsolve_by_lu(T,[0, 0]);
                                 [ - lambda  lambda ]
(%o3)           %%linsolve_by_lu([                  ], [0, 0])
                                 [    mu      - mu  ]
(%i4) A: s*identfor(T) - T;
                           [ lambda + s  - lambda ]
(%o4)                      [                      ]
                           [    - mu      s + mu  ]
(%i5) Ps: [1, 0].invert(A);
      [              s + mu                             lambda               ]
(%o5) [ ---------------------------------  --------------------------------- ]
      [ (s + mu) (lambda + s) - mu lambda  (s + mu) (lambda + s) - mu lambda ]
(%i6) Pf: partfrac(Ps, s);
               [             lambda                      mu        ]
(%o6)  Col 1 = [ ------------------------------- + --------------- ]
               [ (lambda + mu) (lambda + s + mu)   s (lambda + mu) ]
                          [     lambda                    lambda              ]
                  Col 2 = [ --------------- - ------------------------------- ]
                          [ s (lambda + mu)   (lambda + mu) (lambda + s + mu) ]
(%i7) ilt(Pf[1,1], s, t);
                            - t (lambda + mu)
                   lambda %e                        mu
(%o7)              -------------------------- + -----------
                          lambda + mu           lambda + mu
(%i8) ilt(Pf[1,2], s, t);
                                          - t (lambda + mu)
                     lambda      lambda %e
(%o8)              ----------- - --------------------------
                   lambda + mu          lambda + mu
(%i9) M:matrix([-lambda_ac, 0, lambda_ac, 0], [lambda_ba, -(lambda_ba + lambda_bd), 0, lambda_bd], [0, lambda_cb, -lambda_cb, 0], [0, 0, lambda_dc, -lambda_dc]);
      [ - lambda_ac             0              lambda_ac        0      ]
      [                                                                ]
      [  lambda_ba   - lambda_bd - lambda_ba       0        lambda_bd  ]
(%o9) [                                                                ]
      [      0              lambda_cb         - lambda_cb       0      ]
      [                                                                ]
      [      0                  0              lambda_dc   - lambda_dc ]
(%i10) determinant(M);
(%o10) - lambda_ac (lambda_bd lambda_cb lambda_dc
 + (- lambda_bd - lambda_ba) lambda_cb lambda_dc)
 - lambda_ac lambda_ba lambda_cb lambda_dc
(%i11) 
Run Example
declare(lambda, [constant, real, scalar]);
(%o1)                                done
(%i2) assume(lambda >
 0, lambda <
= 1);
(%o2)                    [0 < lambda, lambda - 1 <= 0]
(%i3) declare(mu, [constant, real, scalar]);
(%o3)                                done
(%i4) assume(mu >
 0, mu <
= 1);
(%o4)                        [0 < mu, mu - 1 <= 0]
(%i5) T: matrix([-lambda, lambda], [mu, -mu]);
                             [ - lambda  lambda ]
(%o5)                        [                  ]
                             [    mu      - mu  ]
(%i6) A: s*identfor(T) - T;
                           [ s + lambda  - lambda ]
(%o6)                      [                      ]
                           [    - mu      s + mu  ]
(%i7) Ps: [1, 0].invert(A);
      [              s + mu                             lambda               ]
(%o7) [ ---------------------------------  --------------------------------- ]
      [ (s + mu) (s + lambda) - mu lambda  (s + mu) (s + lambda) - mu lambda ]
(%i8) Pf: partfrac(Ps, s);
               [             lambda                      mu        ]
(%o8)  Col 1 = [ ------------------------------- + --------------- ]
               [ (lambda + mu) (s + lambda + mu)   (lambda + mu) s ]
                          [     lambda                    lambda              ]
                  Col 2 = [ --------------- - ------------------------------- ]
                          [ (lambda + mu) s   (lambda + mu) (s + lambda + mu) ]
(%i9) p0(t) := ilt(Pf[1,1], s, t);
(%o9)                     p0(t) := ilt(Pf    , s, t)
                                         1, 1
(%i10) limit(p0(t), t, inf);
                                      mu
(%o10)                            -----------
                                  lambda + mu
(%i11) p1(t):= ilt(Pf[1,2], s, t);
(%o11)                    p1(t) := ilt(Pf    , s, t)
                                         1, 2
(%i12) limit(p1(t), t, inf);
                                    lambda
(%o12)                            -----------
                                  lambda + mu
(%i13) 

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