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Transition Matrix for Axes Rotation in 3D and 2D | Linear Algebra
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We go over how to transition between the standard set of orthonormal bases for R^2 and R^3 to a rotates set of orthonormal basis vectors for R^2 and R^3 by finding the appropriate transition matrix for the axes rotation. In this way we are able to re-express points (without moving them) relative to the rotated set of orthonormal basis vectors. We'll consider some trigonometry to construct the transition matrix and do some examples of using the resulting rotation equations to express a point in terms of rotated axes. #linearalgebra
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0:00 Intro
0:32 Theorem on Orthogonal Transition Matrices
1:40 Rotation of Axes in 2-Space
7:04 Transition Matrix and Rotation Equations in R^2
8:22 Example of Axes Rotation in R^2
9:40 Rotation of Axes in 3-Space
10:43 Transition Matrix and Rotation Equations in R^3
11:11 Example of Axes Rotation in R^3
12:01 Orthogonality
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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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Join Wrath of Math to get exclusive videos, lecture notes, and more:
0:00 Intro
0:32 Theorem on Orthogonal Transition Matrices
1:40 Rotation of Axes in 2-Space
7:04 Transition Matrix and Rotation Equations in R^2
8:22 Example of Axes Rotation in R^2
9:40 Rotation of Axes in 3-Space
10:43 Transition Matrix and Rotation Equations in R^3
11:11 Example of Axes Rotation in R^3
12:01 Orthogonality
◉Textbooks I Like◉
★DONATE★
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...
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