Sylvester's law of inertia theorem

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  1. Vinayaka Gandadi
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Hi Vinayaka
Congruence matrix has the same signature (positive, negative and zero eigenvalues).
For example matrix A is an symmetric matrix, A, PAP(transpose), QAQ(transpose) all have the same signature (positive, negative and zero eigenvalues).

In this video, you prove M and L are congruence matrix. M can be KLK(transpose). You prove M, L have the same signature.
In your example, M, L both are diagonal matrix. but if G= RLR(transpose), but G is not a diagonal matrix. How to prove G, L have same signature?
Thank you

yunfan
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Sir can you teach first sylow's theoren

believeingodjesus
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Sir please May I know author of this book?

mirriyaz
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Sir can you 🥺 share the book pdf through youtube for reference

believeingodjesus