How would I prove the title statement? My Gilbert Strang Ed. 5 Linear Algebra textbook talks about $LDL^T$ factorization but I don't quite understand it. Online proofs also talk about Sylvester's Law of Inertia - but I can't find any good definitions of it. I've also attempted to try and work out the algebraic expressions for pivots of a symmetric matrix - however at dimensions beyond $3 \times 3$ the operations become far too tedious to complete, however this method did work for $3 \times 3$ matrices and ones of lower dimensions. Help will be appreciated, thanks!
2026-03-28 01:35:32.1774661732
Symmetric matrics have pivots with the same signs as their eigenvalues
111 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in EIGENVALUES-EIGENVECTORS
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