after finding out what geometric multiplicity was, I was surprised to notice that in every question I'd done it was always 1.(adsbygoogle = window.adsbygoogle || []).push({});

So I'm trying to prove an example with g.m. > 1 to see why it works.

I've found a matrix which definitely has an eigenvalue with g.m. = 2. I've checked everything with WolframAlpha, so the following is correct:

Matrix A =

[tex]

\left( \begin{array}{ccc}

5 & 4 & 2 \\

4 & 5 & 2 \\

2 & 2 & 2 \end{array} \right) [/tex]

Determinant = 10

Characteristic polynomial = [tex]-((x-10) (x-1)^2)[/tex]

So eigenvalues =

10

1< -- with a.m. = 2, and g.m. = 2

So find the eigenvectors to find I'd start with:

(A - 1 * I ) v =0, the matrix being:

[tex]

\left( \begin{array}{ccc}

4 & 4 & 2 \\

4 & 4 & 2 \\

2 & 2 & 1 \end{array} \right)[/tex]

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# Geometric multiplicity > 1

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