Symmetric Matrices and their Properties | Linear Algebra

We introduce symmetric matrices. We see examples and nonexamples of symmetric matrices, some basic properties a symmetric matrix has, and see how to produce a symmetric matrix using a matrix and its transpose. We'll also do an example of producing a symmetric with matrix multiplication. We also prove a product of matrices is symmetric if and only if those matrices commute. #linearalgebra

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0:00 Intro
0:15 Definition of Symmetric Matrix
0:39 Examples of Symmetric Matrices
1:45 Nonexamples of Symmetric Matrices
2:27 Properties of Symmetric Matrices
3:24 (AB)^T=AB iff AB=BA
4:38 Invertible Symmetric Matrix
5:23 AA^T and A^TA
9:29 Conclusion

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Thanks to Loke Tan, Raül Beienheimer, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon!

Outro music is mine. You cannot find it anywhere, for now.

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[LL-koqu]

Thank you very much. your playlist on group theory helped me understand it and gave me enough confidence in myself for the finals.

[PunmasterSTP]

Symmetric? More like "Super, and these videos sure do the trick!" 👍

[Israaxgamal]

Loved your video explanation! Would it be possible to get access to the notes/outline you are using? I think having that written material would really help solidify the concepts. Appreciate you considering sharing it.

[alphiephoenix]

ok but wheres the link to the outro song