Theorems in geometry | Theorems in linear algebra
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).
Principal axes theorem + orthogonal matrices
Free ebook http://tinyurl.com/EngMathYT A basic introduction to orthogonal matrices and the principal axes theorem. Several examples are presented involving a simplification of quadratic (quadric) forms. A proof is also given.
From playlist Engineering Mathematics
The Parallel Axis Theorem (Steiner's Theorem) | Classical Mechanics
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
From playlist Classical Mechanics
What is the Consecutive Interior Angle Converse Theorem
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Introduction to the Principal Unit Normal Vector
Introduction to the Principal Unit Normal Vector
From playlist Calculus 3
Algebra - Ch. 0.6: Basic Concepts (3 of 36) What is the Imaginary Axis?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the differences between the imaginary axis and the y-axis. Next video in this series can be seen at: https://youtu.be/I87ZaOAOdog
From playlist ALGEBRA 0.6 BASIC CONCEPTS
CCSS What is an angle bisector
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
CCSS What is the difference between Acute, Obtuse, Right and Straight Angles
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
13. Four Classes of Problems With Rotational Motion
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
What is an angle and it's parts
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Tensor Calculus Lecture 14b: Examples of Curves in 3D
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
11. Mass Moment of Inertia of Rigid Bodies
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
Complex Analysis 08: Using anti-derivatives
Contour integration with anti-derivatives. Three examples
From playlist MATH2069 Complex Analysis
What is an example of lines that are a linear pair
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
Tensor Calculus Lecture 14f: Principal Curvatures
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Year 12/AS Pure Chapter 10.3 (Trigonometric Identities and Equations)
In this video we explore how the CAST diagram can be used to solve trigonometric equations. This lesson is meant as preparation for Exercise 10D, page 216 of the Pearson Edexcel Pure Mathematics Year 1/AS Textbook: bit.ly/PuretextbookYear1 Introduction:
From playlist Year 12/AS Edexcel (8MA0) Mathematics: FULL COURSE
Complex Analysis L07: Analytic Functions Solve Laplace's Equation
This video shows that the real and imaginary parts of analytic complex functions solve Laplace's equation. These are known as harmonic functions. @eigensteve on Twitter eigensteve.com databookuw.com
From playlist Engineering Math: Crash Course in Complex Analysis
16. Kinematic Approach to Finding Generalized Forces
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
Eigenvalues & eigenvectors + applications tutorial
Free ebook http://tinyurl.com/EngMathYT A tutorial showing some of the useful applications of eigenvalues and eigenvectors, including: (i) How they can be used in quadratic forms; (ii) How they can be applied to solve systems of ordinary differential equations.
From playlist Engineering Mathematics
CCSS What is the Angle Addition Postulate
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
From playlist Angle Relationships
12. Problem Solving Methods for Rotating Rigid Bodies
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