Eigenspaces and their Bases | Linear Algebra

We go over what the eigenspace corresponding to an eigenvalue is, we see the definition of eigenspace, several ways to think of eigenspaces, a geometric view of eigenspaces, and do a 2x2 example of finding bases for the eigenspaces and a 3x3 example of finding bases for the eigenspaces. #linearalgebra Linear Algebra course: https://www.youtube.com/playlist?list=PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc Join Wrath of Math to get exclusive videos, music, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join 0:00 Intro 0:20 Definition 1:40 Infinitely Many Eigenvectors 1:56 Alternate Views of Eigenspaces 2:57 Bases for Eigenspaces of 2x2 Matrix 7:53 Geometrical View of Eigenspaces 9:25 Bases for Eigenspaces of 3x3 Matrix 13:55 Conclusion ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.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: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Math Rap channel: https://www.youtube.com/channel/UCQ2UBhg5nwWCL2aPC7_IpDQ/featured