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This document summarizes key concepts from a lecture on linear algebra and differential equations, including: 1) The Cayley-Hamilton theorem states that every matrix satisfies its own characteristic equation. This allows powers and inverses of matrices to be expressed in terms of the matrix and identity. 2) For 3x3 matrices, the Cayley-Hamilton theorem takes the form of A3 − (trA)A2 + CA − (detA)I = 0. 3) The eigenvalues and eigenvectors of symmetric matrices are always real, and eigenvectors correspon
- Author
- Roumen Guha
- Language
- EN