Theorems in geometry | Theorems in linear algebra

Principal axis theorem

In the mathematical fields of geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with an ellipsoid or hyperboloid, generalizing the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular, and gives a constructive procedure for finding them. Mathematically, the principal axis theorem is a generalization of the method of completing the square from elementary algebra. In linear algebra and functional analysis, the principal axis theorem is a geometrical counterpart of the spectral theorem. It has applications to the statistics of principal components analysis and the singular value decomposition. In physics, the theorem is fundamental to the studies of angular momentum and birefringence. (Wikipedia).

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From playlist Engineering Mathematics

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In this video, we will derive the parallel axis theorem of classical mechanics! References: [1] Demtröder, "Mechanics and Thermodynamics", Springer (2017). Follow us on Instagram: https://www.instagram.com/prettymuchvideo/ If you want to help us get rid of ads on YouTube, you can sup

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Introduction to the Principal Unit Normal Vector

Introduction to the Principal Unit Normal Vector

From playlist Calculus 3

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From playlist ALGEBRA 0.6 BASIC CONCEPTS

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MIT 2.003SC Engineering Dynamics, Fall 2011 View the complete course: http://ocw.mit.edu/2-003SCF11 Instructor: J. Kim Vandiver License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 2.003SC Engineering Dynamics, Fall 2011

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From playlist MIT 2.003SC Engineering Dynamics, Fall 2011

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16. Kinematic Approach to Finding Generalized Forces

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From playlist MIT 2.003SC Engineering Dynamics, Fall 2011

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CCSS What is the Angle Addition Postulate

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12. Problem Solving Methods for Rotating Rigid Bodies

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From playlist MIT 2.003SC Engineering Dynamics, Fall 2011

Related pages

Functional analysis | Linear algebra | Ellipse | Spectral theorem | Statistics | Ellipsoid | Sylvester's law of inertia | Homogeneous polynomial | Angular momentum | Singular value decomposition | Rotational symmetry | Mathematics | Euclidean space | Symmetric matrix | Hyperbola | Orthogonal matrix | Hyperboloid | Geometry | Elementary algebra | Completing the square