Re: I am trying to determine eigenvalues for an nxn matrix where n>2

From: Dana DeLouis <ddelouis_at_bellsouth.net>
Date: Sat, 1 Jul 2006 18:48:59 -0400

> 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" <Mark_at_discussions.microsoft.com> wrote in message 
news:58648AF5-D617-4036-8A33-479263C5807A_at_microsoft.com...


> basically I am trying to determine the math steps for determining the

> eigenvalues for a nxn matrix where n= either 3 or 4. 

Received on Sat Jul 01 2006 - 15:48:59 PDT