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Question: Just curious (not necessarily a Maple‑related question)

Question:Just curious (not necessarily a Maple‑related question)

Harry Garst 269 Maple
linear-algebra adjoint
2 hours ago
0

I was wondering which theorem the following result is based on, and what the name of the sequence used is.

Adjoint353.mw

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restart; with(LinearAlgebra)
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K := proc (i::integer, j::integer) local M; M := Matrix(5, 5); M[i, i] := 1; M[j, j] := 1; return M end proc
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F := proc (r, c, g, h) options operator, arrow; Adjoint(A.K(r, c).B.K(g, h).C) end proc
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d1 := 3; d2 := 5; A := Matrix(d1, d2, symbol = a); B := Matrix(d2, d2, symbol = b); C := Matrix(d2, d1, symbol = c)

d1 := 3

  

d2 := 5

  

Matrix(3, 5, {(1, 1) = a[1, 1], (1, 2) = a[1, 2], (1, 3) = a[1, 3], (1, 4) = a[1, 4], (1, 5) = a[1, 5], (2, 1) = a[2, 1], (2, 2) = a[2, 2], (2, 3) = a[2, 3], (2, 4) = a[2, 4], (2, 5) = a[2, 5], (3, 1) = a[3, 1], (3, 2) = a[3, 2], (3, 3) = a[3, 3], (3, 4) = a[3, 4], (3, 5) = a[3, 5]})

  

Matrix(5, 5, {(1, 1) = b[1, 1], (1, 2) = b[1, 2], (1, 3) = b[1, 3], (1, 4) = b[1, 4], (1, 5) = b[1, 5], (2, 1) = b[2, 1], (2, 2) = b[2, 2], (2, 3) = b[2, 3], (2, 4) = b[2, 4], (2, 5) = b[2, 5], (3, 1) = b[3, 1], (3, 2) = b[3, 2], (3, 3) = b[3, 3], (3, 4) = b[3, 4], (3, 5) = b[3, 5], (4, 1) = b[4, 1], (4, 2) = b[4, 2], (4, 3) = b[4, 3], (4, 4) = b[4, 4], (4, 5) = b[4, 5], (5, 1) = b[5, 1], (5, 2) = b[5, 2], (5, 3) = b[5, 3], (5, 4) = b[5, 4], (5, 5) = b[5, 5]})

  

Matrix(%id = 36893489807004764868)

 (1)
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simplify(Adjoint(A.B.C)-add([F(1, 2, 1, 2), F(1, 2, 1, 3), F(1, 2, 1, 4), F(1, 2, 1, 5), F(1, 2, 2, 3), F(1, 2, 2, 4), F(1, 2, 2, 5), F(1, 2, 3, 4), F(1, 2, 3, 5), F(1, 2, 4, 5), F(1, 3, 1, 2), F(1, 3, 1, 3), F(1, 3, 1, 4), F(1, 3, 1, 5), F(1, 3, 2, 3), F(1, 3, 2, 4), F(1, 3, 2, 5), F(1, 3, 3, 4), F(1, 3, 3, 5), F(1, 3, 4, 5), F(1, 4, 1, 2), F(1, 4, 1, 3), F(1, 4, 1, 4), F(1, 4, 1, 5), F(1, 4, 2, 3), F(1, 4, 2, 4), F(1, 4, 2, 5), F(1, 4, 3, 4), F(1, 4, 3, 5), F(1, 4, 4, 5), F(1, 5, 1, 2), F(1, 5, 1, 3), F(1, 5, 1, 4), F(1, 5, 1, 5), F(1, 5, 2, 3), F(1, 5, 2, 4), F(1, 5, 2, 5), F(1, 5, 3, 4), F(1, 5, 3, 5), F(1, 5, 4, 5), F(2, 3, 1, 2), F(2, 3, 1, 3), F(2, 3, 1, 4), F(2, 3, 1, 5), F(2, 3, 2, 3), F(2, 3, 2, 4), F(2, 3, 2, 5), F(2, 3, 3, 4), F(2, 3, 3, 5), F(2, 3, 4, 5), F(2, 4, 1, 2), F(2, 4, 1, 3), F(2, 4, 1, 4), F(2, 4, 1, 5), F(2, 4, 2, 3), F(2, 4, 2, 4), F(2, 4, 2, 5), F(2, 4, 3, 4), F(2, 4, 3, 5), F(2, 4, 4, 5), F(2, 5, 1, 2), F(2, 5, 1, 3), F(2, 5, 1, 4), F(2, 5, 1, 5), F(2, 5, 2, 3), F(2, 5, 2, 4), F(2, 5, 2, 5), F(2, 5, 3, 4), F(2, 5, 3, 5), F(2, 5, 4, 5), F(3, 4, 1, 2), F(3, 4, 1, 3), F(3, 4, 1, 4), F(3, 4, 1, 5), F(3, 4, 2, 3), F(3, 4, 2, 4), F(3, 4, 2, 5), F(3, 4, 3, 4), F(3, 4, 3, 5), F(3, 4, 4, 5), F(3, 5, 1, 2), F(3, 5, 1, 3), F(3, 5, 1, 4), F(3, 5, 1, 5), F(3, 5, 2, 3), F(3, 5, 2, 4), F(3, 5, 2, 5), F(3, 5, 3, 4), F(3, 5, 3, 5), F(3, 5, 4, 5), F(4, 5, 1, 2), F(4, 5, 1, 3), F(4, 5, 1, 4), F(4, 5, 1, 5), F(4, 5, 2, 3), F(4, 5, 2, 4), F(4, 5, 2, 5), F(4, 5, 3, 4), F(4, 5, 3, 5), F(4, 5, 4, 5)]))

Matrix(%id = 36893489807027993164)

 (2)
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nops([F(1, 2, 1, 2), F(1, 2, 1, 3), F(1, 2, 1, 4), F(1, 2, 1, 5), F(1, 2, 2, 3), F(1, 2, 2, 4), F(1, 2, 2, 5), F(1, 2, 3, 4), F(1, 2, 3, 5), F(1, 2, 4, 5), F(1, 3, 1, 2), F(1, 3, 1, 3), F(1, 3, 1, 4), F(1, 3, 1, 5), F(1, 3, 2, 3), F(1, 3, 2, 4), F(1, 3, 2, 5), F(1, 3, 3, 4), F(1, 3, 3, 5), F(1, 3, 4, 5), F(1, 4, 1, 2), F(1, 4, 1, 3), F(1, 4, 1, 4), F(1, 4, 1, 5), F(1, 4, 2, 3), F(1, 4, 2, 4), F(1, 4, 2, 5), F(1, 4, 3, 4), F(1, 4, 3, 5), F(1, 4, 4, 5), F(1, 5, 1, 2), F(1, 5, 1, 3), F(1, 5, 1, 4), F(1, 5, 1, 5), F(1, 5, 2, 3), F(1, 5, 2, 4), F(1, 5, 2, 5), F(1, 5, 3, 4), F(1, 5, 3, 5), F(1, 5, 4, 5), F(2, 3, 1, 2), F(2, 3, 1, 3), F(2, 3, 1, 4), F(2, 3, 1, 5), F(2, 3, 2, 3), F(2, 3, 2, 4), F(2, 3, 2, 5), F(2, 3, 3, 4), F(2, 3, 3, 5), F(2, 3, 4, 5), F(2, 4, 1, 2), F(2, 4, 1, 3), F(2, 4, 1, 4), F(2, 4, 1, 5), F(2, 4, 2, 3), F(2, 4, 2, 4), F(2, 4, 2, 5), F(2, 4, 3, 4), F(2, 4, 3, 5), F(2, 4, 4, 5), F(2, 5, 1, 2), F(2, 5, 1, 3), F(2, 5, 1, 4), F(2, 5, 1, 5), F(2, 5, 2, 3), F(2, 5, 2, 4), F(2, 5, 2, 5), F(2, 5, 3, 4), F(2, 5, 3, 5), F(2, 5, 4, 5), F(3, 4, 1, 2), F(3, 4, 1, 3), F(3, 4, 1, 4), F(3, 4, 1, 5), F(3, 4, 2, 3), F(3, 4, 2, 4), F(3, 4, 2, 5), F(3, 4, 3, 4), F(3, 4, 3, 5), F(3, 4, 4, 5), F(3, 5, 1, 2), F(3, 5, 1, 3), F(3, 5, 1, 4), F(3, 5, 1, 5), F(3, 5, 2, 3), F(3, 5, 2, 4), F(3, 5, 2, 5), F(3, 5, 3, 4), F(3, 5, 3, 5), F(3, 5, 4, 5), F(4, 5, 1, 2), F(4, 5, 1, 3), F(4, 5, 1, 4), F(4, 5, 1, 5), F(4, 5, 2, 3), F(4, 5, 2, 4), F(4, 5, 2, 5), F(4, 5, 3, 4), F(4, 5, 3, 5), F(4, 5, 4, 5)])

100

 (3)
 

NULL

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