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#1
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I am trying to determine eigenvalues for an nxn matrix where n2
basically I am trying to determine the math steps for determining the
eigenvalues for a nxn matrix where n= either 3 or 4. |
#2
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I am trying to determine eigenvalues for an nxn matrix where n2
Eigenvalues for a n x n matrix where n= either 3 or 4.
If you don't get a better response to a 3 by 3 matrix, here's a brute force method to calculate the Characteristic Polynomial. You then call a routine that Solves the cubic Equation with the following coefficients. Here, 'a is assumed to be 1. Sub Demo() Dim m Dim b, c, d Dim Det m = [A1:C3] 'A future item to check... 'If Det = 0 then... Det = WorksheetFunction.MDeterm(m) '//======================================= '// Characteristic Polynomial = '// x^3 + b*x^2 + c*x + d = 0 '//======================================= b = -(m(1, 1) + m(2, 2) + m(3, 3)) c = m(1, 1) * m(2, 2) - m(1, 3) * m(3, 1) - _ m(2, 3) * m(3, 2) + m(1, 1) * m(3, 3) + _ m(2, 2) * m(3, 3) - m(1, 2) * m(2, 1) d = m(1, 3) * m(2, 2) * m(3, 1) - _ m(1, 2) * m(2, 3) * m(3, 1) - _ m(1, 3) * m(2, 1) * m(3, 2) + _ m(1, 1) * m(2, 3) * m(3, 2) + _ m(1, 2) * m(2, 1) * m(3, 3) - _ m(1, 1) * m(2, 2) * m(3, 3) Debug.Print b Debug.Print c Debug.Print d End Sub -- HTH. :) Dana DeLouis Windows XP, Office 2003 "Mark" wrote in message ... basically I am trying to determine the math steps for determining the eigenvalues for a nxn matrix where n= either 3 or 4. |
#3
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I am trying to determine eigenvalues for an nxn matrix where n2
It looks like the longer equation for d can be reduced...
Change: d = m(1, 3) * m(2, 2) * m(3, 1) ...etc to: Det = WorksheetFunction.MDeterm(m) d = -Det -- HTH. :) Dana DeLouis Windows XP, Office 2003 <snip |
#4
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I am trying to determine eigenvalues for an nxn matrix where n2
For a 3x3 matrix, this might be slightly better to calculate the 3 variables
in the cubic equation. You then solve the cubic equation to get your 3 Eigenvalues. I'm not exactly sure how it's done for larger systems. Sub Demo() Dim m Dim b, c, d Dim j, p, n '// Load array from A1:C3 m = [A1:C3] '//======================================= '// Characteristic Polynomial = '// x^3 + b*x^2 + c*x + d = 0 '//======================================= For j = 1 To 3 b = b - m(j, j) 'Trace p = 163 Mod (j + 4) n = 11 Mod (j + 2) 'Minors c = c + m(p, p) * m(n, n) - m(p, n) * m(n, p) Next j d = -WorksheetFunction.MDeterm(m) Debug.Print b; c; d End Sub -- HTH. :) Dana DeLouis Windows XP, Office 2003 <snip |
#5
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I am trying to determine eigenvalues for an nxn matrix where n2
OK... I am assuming that this is a macro code. Let me give it a whirl.
Thanks for the help. I'll let you know how it worked. thanks, "Mark" wrote: basically I am trying to determine the math steps for determining the eigenvalues for a nxn matrix where n= either 3 or 4. |
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