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.