Quadratic form with a matrix

For the book, you may refer: amzn.to/3aT4ino
This lecture explains the quadratic form and their definiteness such as positive definite, positive semi-definite, negative definite, negative semi-definite, and indefiniteness.
Other videos:
Quadratic form: • Quadratic form with a ...
Hessian Matrix: • Hessian Matrix of a fu...
Convex & Concave function: • Convex and Concave Fun...
Maxima & Minima of the function: • Maxima and Minima of t...

[@thedivinemathematics9547]

Many books have given this wrong information as well. Actually, for positive semidefinite we need to check sign of "leading principle minors" while for positive semidefinite we need to check sign of all "principle minors". Hermitian matrix is the most generalized case of symmetric matrices. So,
1. a Hermitian matrix M is positive-semidefinite if and only if all "principal minors" of M are nonnegative.
2. a Hermitian matrix M is positive-definite if and only if all the "leading principal minors" are positive.
For more details please : en.wikipedia.org/wiki/Sylvester%27s_criterion#:~:text=Sylvester's%20Criterion%3A%20The%20real%2Dsymmetric,minors%20of%20A%20are%20positive.

[@divyamverma2606]

I think you wrote "semi" definite for both Leading principal minor and principal minor by mistake. BTW thanks !

[@Thoni-op9kq5em8s]

Very nice
Thank you so much.
Please continue to upload more videos.
Worth the time spending here.

[@user-np7rn2rc5t]

Great job!

[@thedivinemathematics9547]

If I take a Symmetric Matrix, such that, a11=4, a22=1, a33= -1 ,a12= 2, a13= -1, a23= -0.5. Then the first leading principal minor is 4, while other two leading principal minors are 0. Then by the principle minor rule (Sylvester's Rule) this matrix should be positive semidefinite. But actually this is indefinite.

[@owji414]

Thank you very much sir, your explanation is really helpful for my exam tomorrow, it's really nice you gave a lot of examples

[@DrHarishGarg]

My pleasure ... Kindly share with other too

[@divyamverma2606]

At 14:32, I think there is some error in the approach, because if we visualise the graph on 3d calculator, the function value is positive for non zero x_1 and x_2 , hence it can't be negative definite.
For example, x_1 =0 and x_2 = 2 , f(x_1,x_2) = 4

[@RAHUDAS]

Thanks sir , I came across your video it is great help and super clear for me . Kindly provide some links to read further on same topic

[@piyushmaurya3335]

Well explained

[@ETHIOPIAN-OLD-MUSIC-3533]

thank you sir !

[@explicacaoonline]

Thank you so much, the best video on the subject!

[@DrHarishGarg]

Thanks Andre ... Kindly share with others too

[@ashvinlovepatidar]

So much helpful ,😊

[@fatematuzzohra5370]

Got it. Thank you sir

[@user-zy8nz6bc6q]

Great sir, heads of

[@sushmitagupta5069]

Thank you 😊it helped a lot.

[@shikhasarkar4552]

Thank you sir

[@kindykomal]

Really great explanation sir 🙏🏻

[@DrHarishGarg]

Thanks.

[@aishwaryajamineesahoo9032]

Nicely explained 😊😊😊😊

[@DrHarishGarg]

My pleasure... Keep watching.

[@prathameshekal7308]

Tq

[@DrHarishGarg]

Welcome

[@ahaanfarooq3556]

love u

[@DrHarishGarg]

Thank you ❤

[@m.syarifudinalrasyid9377]

Could you simulink the queen honey bee migration algorithms please?

[@kevinm8607]

Tau 2x2 ka bhi to batao
D1, d2 aur d3 kya hoga?
Why to give half knowledge?