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9:10
YouTube
Math Mastery with Amitesh
Proof that EVERY matrix is the root of a polynomial! | Linear Algebra Theory!
If A is an n x n matrix and p(x) = c_k x^k + ... + c_1 x + c_0 is a polynomial, then p(A) = c_k A^k + ... + c_1 A + c_0 I (where I is the identity n x n matrix). We say that A is a root of p(x) if p(A) = 0 (the zero matrix). In this video, we prove that every n x n matrix is the root of a non-zero polynomial of degree ≤ n^2. The proof is a ...
421 views
2 weeks ago
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