Consider two matrices: A = egin{bmatrix} 5 & 3 \ 3 & 5 end{bmatrix}, B = egin{bmatrix} -13 & -8 & -4 \ 12 & 7 & 4 \ 24 & 16 & 7 end{bmatrix} a) Find the eigenvalues and corresponding eigenvectors of matrix A without using any computing software b) Find the eigendecomposition of matrix A as A=Q?Q^T using the results from 3.a c) Find the eigenvalues and corresponding eigenvectors of matrix B using Python NumPy package. d) Find the definiteness of matrices A and B.
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Matrix A - λI is: $$ \begin{pmatrix} -13-\lambda & -8 & 15 \\ 3 & 12-\lambda & 5 \\ 24 & 16 & -\lambda \end{pmatrix} $$ Now, we find the determinant of this matrix: $$ \begin{vmatrix} -13-\lambda & -8 & 15 \\ 3 & 12-\lambda & 5 \\ 24 & 16 & Show more…
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Consider two matrices: a) Find the eigenvalues and corresponding eigenvectors of matrix A without using any computing software b) Find the eigendecomposition of matrix A as A=QAQ^T using the results from 3.a c) Find the eigenvalues and corresponding eigenvectors of matrix B using Python NumPy package. d) Find the definiteness of matrices A and B.
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