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Book: Rotations


See: Math notebook, Define classical Lie groups, Classical Lie groups

Understand Lie groups in terms of rotations.


Understand numbers

Understand matrices

Understand how real rotations and their axes chain together real dimensions.

Understand rotations in complex dimensions and quaternionic dimensions.

Understand how, in general, rotations and their axes chain together dimensions.

Linear algebra

Geometry

Advanced mathematical ideas

Perspectives


Mathematical facts

Numbers

Norm-preserving matrices

Rotation matrices

Transpose

The relevant complex matrices.

{$\Omega = \begin{bmatrix} 0 & I_n \\ -I_n & 0 \\ \end{bmatrix}$}

Combinatorics

Ideas

Geometry

Polytopes define axes of rotations and related geometrical frameworks. They define different ways of describing opposite directions of rotation.

Oriented areas are swept out by rotations and the axis can be placed anywhere inside the area of the triangle.

Readings

Wikipedia

Other

Parsiųstas iš http://www.ms.lt/sodas/Book/Rotations
Puslapis paskutinį kartą pakeistas 2019 gegužės 18 d., 17:50