Math Problem Statement
make a formal proof to show If P is a 2 × 2 stochastic matrix, with second eigenvalue λ not equal to 1 or -1, show that v1 + v2 = 0 where v P = λv and v = (v1, v2)
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Eigenvalues
Stochastic Matrices
Formulas
v P = λv
P = [[p11, p12], [p21, p22]]
det(P - λI) = 0
Theorems
Perron-Frobenius Theorem
Suitable Grade Level
Grades 11-12
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