Math Problem Statement
diagonalize the matrix orthogonally a= [ 3 -1 1, -1 5 -1, 1 -1 3 ]
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Diagonalization
Eigenvalues and Eigenvectors
Orthogonality
Formulas
Characteristic equation det(A - λI) = 0
Eigenvector equation (A - λI)v = 0
Orthogonal matrix condition P^T P = I
Diagonalization formula A = P D P^T
Theorems
Spectral Theorem: A real symmetric matrix can be orthogonally diagonalized
Eigenvalue Theorem: The eigenvalues of a matrix are found by solving the characteristic equation
Suitable Grade Level
Undergraduate (Linear Algebra)
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