Math Problem Statement
what is your interpretation of tr(A²)? Without direct calculations, find one of the eigenvalues of A based on the information you can get from A. Then calculate it's corresponding eigenvector.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Theory
Eigenvalues and Eigenvectors
Formulas
tr(A^2) = λ1^2 + λ2^2 + ... + λn^2
tr(A) = λ1 + λ2 + ... + λn
A * v = λ * v
Theorems
Eigenvalue Decomposition
Trace of a Matrix Theorem
Suitable Grade Level
Undergraduate