Math Problem Statement
prove that the matrix is orthogonal
Prove that the matrix P is orthogonal.
Solution
To prove that the matrix is orthogonal, we need to show that:
where is the transpose of , and is the identity matrix.
Given the matrix ( P
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Theory
Orthogonal Matrices
Formulas
P^T P = I
Matrix Transposition
Identity Matrix
Theorems
Orthogonality Theorem for Matrices
Suitable Grade Level
Grades 11-12, Undergraduate