The LDU and LDLᵀ Decompositions and the Implications for Positive Definiteness

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lem.ma/LA - Linear Algebra on Lemma
bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook
lem.ma/prep - Complete SAT Math Prep

[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@andinosa]

Your videos have reignited my love for mathematics. I've started an MSC in numerical methods online. Pdes and linear algebra are truly fascinating. Keep up the deep conceptual videos. Love them!

[@thetedmang]

Watched your whole series some time ago but I always find myself coming back to it for pointers; thanks Dr. Grinfeld!

[@justinoboyle5767]

Another extremely helpful video. Thank you

[@SecretWeasel1]

1:42 When you're about to get MTF surgery but you're having second thoughts

[@AJ-et3vf]

Awesome video! Thank you!

[@Robocat754]

I'd like everything to be accurate. When you said if all the entries in the first 2 matrices are nonzero the 2 by 2 result matrix will pull in stuffs in the third column and third row of the last matrix. But it only pulls the first 2 columns in the third row of the last matrix. The entries in the third column will stay in the third column. But it will pull in the third column of the second matrix since this is the matrix where each column does row combination of the third matrix.

[@Robocat754]

Correct: Each row does row combination of the third matrix.

[@BleachWizz]

yaknow one thing I'd like to see, that I don't seem to find and I'd love a reference to. These classes using einstein notation and tensor calculus, instead of matrices. Because when we learn tensor we're assumed to understand linear algebra and matrices, so I found some tensor calculus classes and I am having to fall back to these classes to try imagining how I'll carry what they always claims to be true throughout the operations in that new notation or on the idea that vectors are partial derivatives. All this development is hidden on the advanced part of linear algebra, thus not easy to follow and find. This classes are giving me brilliant insights on why tensors actually works the way they do, but sadly I'm struggling with "translating" the proof to tensor notation.

[@MathTheBeautiful]

Hi Kostynha, I agree with you. In the next version of my book, these issues will be addressed more carefully. If you reach out to me by email, I'll send you a few sample chapters. Pavel

[@jessicatolosabaides2767]

Gracias desde España, nos ha sido muy útil.

[@MathTheBeautiful]

¡De nada!

[@y.s753]

what will be left of you after you factor out this D? 1:41

[@tempvariable]

Thanks

[@amoludawant2316]

no understand

[@redafalhi7664]

thank you

[@작은방-e5v]

thanks