- #1
trap101
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Verify the spectral thrm for the symmetric matrix, by finding an orthonormal basis of the apporpriate vector space, the change of basis matrix to this basis and the spectral decmoposition.
Well I've found everything else. We started with the matrix A.
A = \begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix}
Change of basis matrix obtained w.r.t to the eigenvalues: -1, 5:
\begin{bmatrix} -√2/2 & √2/2 \\ √2/2 & √2/2 \end{bmatrix}
the basis from the eigenvalues was:
eigenvalue (-1): ( -√2/2,√2/2) eigenvalue (5): (√2/2,√2/2)
Now I know to obtain the projection you usually use:
[itex]\sum[/itex]<x,wi> wi where x is the vector your looking to project from and w is the basis vectors.
I've been at it for an hr and I can't figure out the matrix of the projection in order to write out the decomposition of matirx A. How do I get those coefficients? Please before I jump off a cliff.
Thanks
Well I've found everything else. We started with the matrix A.
A = \begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix}
Change of basis matrix obtained w.r.t to the eigenvalues: -1, 5:
\begin{bmatrix} -√2/2 & √2/2 \\ √2/2 & √2/2 \end{bmatrix}
the basis from the eigenvalues was:
eigenvalue (-1): ( -√2/2,√2/2) eigenvalue (5): (√2/2,√2/2)
Now I know to obtain the projection you usually use:
[itex]\sum[/itex]<x,wi> wi where x is the vector your looking to project from and w is the basis vectors.
I've been at it for an hr and I can't figure out the matrix of the projection in order to write out the decomposition of matirx A. How do I get those coefficients? Please before I jump off a cliff.
Thanks