In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative. In linear algebra, a real symmetric matrix represents a self-adjoint operator represented in an orthonormal basis over a real inner product space. The corresponding object for a complex inner product space is a Hermitian matrix with complex-valued entries, which is equal to its conjugate transpose. Therefore, in linear algebra over the complex numbers, it is often assumed that a symmetric matrix refers to one which has real-valued entries. Symmetric matrices appear naturally in a variety of applications, and typical numerical linear algebra software makes special accommodations for them. (Wikipedia).
Symmetric matrices - eigenvalues & eigenvectors
Free ebook http://tinyurl.com/EngMathYT A basic introduction to symmetric matrices and their properties, including eigenvalues and eigenvectors. Several examples are presented to illustrate the ideas. Symmetric matrices enjoy interesting applications to quadratic forms.
From playlist Engineering Mathematics
Diagonalizing a symmetric matrix. Orthogonal diagonalization. Finding D and P such that A = PDPT. Finding the spectral decomposition of a matrix. Featuring the Spectral Theorem Check out my Symmetric Matrices playlist: https://www.youtube.com/watch?v=MyziVYheXf8&list=PLJb1qAQIrmmD8boOz9a8
From playlist Symmetric Matrices
Symmetric Matrix | Don't Memorise
This video explains the concept of a Symmetric Matrix. ✅To learn more about, Matrices, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=IBgXO5qvbrg&utm_term=%7Bkeyword%7D In this video, we will learn:
From playlist Matrices
Linear Algebra - Lecture 41 - Diagonalization of Symmetric Matrices
In this lecture, we investigate the diagonalization of symmetric matrices.
From playlist Linear Algebra Lectures
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Linear Algebra 11z: Introduction to Symmetric Matrices
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
Example of Skew-Symmetric Matrix
Matrix Theory: Let a be an invertible skew-symmetric matrix of size n. Show that n is even, and then show that A^{-1} is also skew-symmetric. We show the identities (AB)^T = B^T A^T and (AB)^{-1} = B^{-1}A^{-1}.
From playlist Matrix Theory
Matrices: Transpose and Symmetric Matrices
This is the third video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with matrix transpose and symmetric matrices. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
Nonlinear algebra, Lecture 8: "Tensors", by Bernd Sturmfels and Mateusz Michalek
This is the eight lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Linear Algebra 1.7 Diagonal, Triangular, and Symmetric Matrices
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 32. Quiz 3 Review License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/t
From playlist MIT 18.06 Linear Algebra, Spring 2005
Symmetric and skew symmetric matricies (Ch5 Pr15)
Here we show that A+A^T and AA^T are symmetric matrices, and A-A^T is skew symmetric for A is a square matrix. Presented by N J Wildberger of the School of Mathematics and Statistics, Faculty of Science, UNSW.
From playlist Mathematics 1A (Algebra)
Lec 28 | MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008
Lecture 28: Normal and local modes. High overtone spectra Instructor: Robert Field View the complete course: http://ocw.mit.edu/5-80F08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008
Lecture 16 | Introduction to Linear Dynamical Systems
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the use of symmetric matrices, quadratic forms, matrix norm, and SVDs in LDS for the course Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and l
From playlist Lecture Collection | Linear Dynamical Systems
Transpose matrix | Lecture 4 | Matrix Algebra for Engineers
Definition of the transpose. How to take the transpose of the product of two matrices. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.yout
From playlist Matrix Algebra for Engineers
Skew-symmetric Matrix | Don't Memorise
This video explains the concept of a Skew-Symmetric Matrix. ✅To learn more about, Matrices, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=uKPmyG18N7I&utm_term=%7Bkeyword%7D In this video, we will le
From playlist Matrices
7F Diagonal Triangular Symmetric Matrices
Diagonal, triangular, and symmetric matrices.
From playlist Linear Algebra
Tensor Calculus 12c: The Self-Adjoint Property in Tensor Notation
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