Complex, Hermitian, and Unitary Matrices

Remember when we talked about complex and imaginary numbers? All that a + bi stuff, it was a while ago. Well that can apply to matrices as well! We've been looking at real matrices thus far, but we can have imaginary or complex matrices if we have imaginary or complex terms as entries. What can we do with these? We can find the complex conjugate, we can find the conjugate transpose, we can check to see if matrices are Hermitian, or unitary, lots of stuff! Let's give it a try.

Script by Howard Whittle

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[ProfessorDaveExplains]

Whoops! In the checking comprehension for question 1, the top right entry on that matrix should be 2 + i, not 2 + 1. Sorry!

[sofiyaprincy]

Professor Dave, I have a topic in my linear algebra and matrix paper called 'Nature of characteristic roots in case of special matrix' . Could you please post on that topic?

[charmy]

He knows a lot about all kinds of stuff! Professor Dave Explains~~~

[allisonphysics]

Thanks for saving me once again Prof. Dave! If you ever add to this series can you cover the following: Symmetric bilinear forms, sesquilinear forms, adjoint/ self-adjoint linear maps, the spectral theorem, Jordan Canonical Form, and positive self-adjoint linear maps.

[ZaChousenWan]

"Change the sign of each imaginary number on the matrix and turn the rows into columns." vs " Show the Transpose of the Complex Conjugate of the given Matrix."

Good teachers vs sadistic teachers.

[sanjana]

In the comprehension question no.1 in the 1st row 2nd column it was written 2+1 but in the answer you have written it in the form of conjugate transpose 2-i

[keshosingh]

explained in very simple and lucid style. thank for the video

[dayanulalam]

4:56 the linear algebra Jesus confirmed

[송영찬-zt]

한글자막 누가 달았는지는 모르겠지만 감사합니다
Thank you very much for the Korean subtitles!!

[mohammadamanalimyzada]

Thank you so much for the amazing series
I have learned many things from it

[yashaggarwal]

Doubt :: i need to find adjoint of Matrix, matrix comprises of Complex elements so
What i have to do ? I mean I just have to transpose the matrix or to take its conjugate transpose?

[emlmm]

Really liking these math videos. You should do a series on modern algebra as well.

[Alexandra-heol]

I needed linear algebra for better understanding the data science algorithms. Thanks for the well-structured and clear course!

[huythai]

thank you so much it's very clear to understand

[interresistance]

2nd one is Not Hermitian
3rd one will be Not Unitary!!

[arinalikes]

U gotta way to make things lucid, thank you sm ❤

[harishbalaji]

Professor Dave it was really pakka, crystal clear

[manjusulekha]

Second...🙋very usefull video...thank you sir...

[Tomas-zvjs]

Hey how is the conjugate of that original matrix in the first example not -7 but remains as seven but all the other terms have their signs flipped?

[alfandosavant]

2nd week of engineering major and I need to recall this. Thank you so much!