Quadratic form with a matrix

This lecture explains the quadratic form and their definiteness such as positive definite, positive semi-definite, negative definite, negative semi-definite, and indefiniteness.
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[thedivinemathematics]

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.

[kevinm]

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

[divyamverma]

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

[thedivinemathematics]

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.

[Thoni-opkqems]

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

[owji]

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

[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

[m.syarifudinalrasyid]

Could you simulink the queen honey bee migration algorithms please?

[explicacaoonline]

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