Wrath of Math | Show Two Matrices are Orthogonal | Linear Algebra Exercises @WrathofMath | Uploaded 2 months ago | Updated 6 hours ago
We show two matrices are orthogonal with respect to the standard inner product on the space of 2 by 2 matrices. For two matrices U and V this involves taking the trace of the product of U transpose with V. We see this is 0, hence the matrices are orthogonal in this inner product space. #linearalgebra
Inner Product Space (introduces standard inner product on matrices): youtu.be/RWLhjq2rfcw
Angles and Orthogonality: youtu.be/lKeYpwQER-M
Linear Algebra course: youtube.com/playlist?list=PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG
Linear Algebra exercises: youtube.com/playlist?list=PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc
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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!
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We show two matrices are orthogonal with respect to the standard inner product on the space of 2 by 2 matrices. For two matrices U and V this involves taking the trace of the product of U transpose with V. We see this is 0, hence the matrices are orthogonal in this inner product space. #linearalgebra
Inner Product Space (introduces standard inner product on matrices): youtu.be/RWLhjq2rfcw
Angles and Orthogonality: youtu.be/lKeYpwQER-M
Linear Algebra course: youtube.com/playlist?list=PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG
Linear Algebra exercises: youtube.com/playlist?list=PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc
Join Wrath of Math to get exclusive videos, music, and more:
youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join
◉Textbooks I Like◉
Graph Theory: amzn.to/3JHQtZj
Real Analysis: amzn.to/3CMdgjI
Abstract Algebra: amzn.to/3IjoZaO
Linear Algebra: amzn.to/43xAWEz
Calculus: amzn.to/3PieD1M
Proofs and Set Theory: amzn.to/367VBXP (available for free online)
Statistics: amzn.to/3tsaEER
Discrete Math: amzn.to/3qfhoUn
Number Theory: amzn.to/3JqpOQd
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: patreon.com/join/wrathofmathlessons
◆ Donate on PayPal: paypal.me/wrathofmath
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.
Follow Wrath of Math on...
● Instagram: instagram.com/wrathofmathedu
● Facebook: facebook.com/WrathofMath
● Twitter: twitter.com/wrathofmathedu
My Math Rap channel: youtube.com/channel/UCQ2UBhg5nwWCL2aPC7_IpDQ/featured
