Lec-3: Trace, Transpose & Conjugate of Matrix | Linear Algebra

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[snape]

Trace of a matrix

For Trace of a matrix
- matrix should be SQUARE matrix
- sum of elements of principal diagonal is called trace of a matrix.

Properties of Trace of a matrix

--> Tr(k.A) = k. Tr(A)
--> Tr( A + B ) = Tr(A) + Tr(B)
--> Tr(AB) = Tr(BA)


Transpose of a matrix

Exchange row elements with colum elements

( A^T ) ^ T = A

(k.A)^T = k.(A^T)

(AB) ^T = (B^T A^T )

( ABC ) ^T = C^T B^T A^T

[Funnyfacts]

Sir please make playlist on web programming ❤thank you sir
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[aishwaryagandhi]

Understood the concepts, thank you sir. 😃

[alsawahashmi]

Thankyou sir ❤ I'm eagerly waiting for your upcoming videos