Symplectic geometry | Matrices
In mathematics, a symplectic matrix is a matrix with real entries that satisfies the condition where denotes the transpose of and is a fixed nonsingular, skew-symmetric matrix. This definition can be extended to matrices with entries in other fields, such as the complex numbers, finite fields, p-adic numbers, and function fields. Typically is chosen to be the block matrix where is the identity matrix. The matrix has determinant and its inverse is . (Wikipedia).
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
LU decomposition of a matrix using sympy
In this video I show you how simple it is to do LU decomposition using sympy in python. I also show you a new way of importing sympy functions so that we do not have to use the sym abbreviation. Lastly we use a Boolean question to see whether the multiplication of the lower and upper tri
From playlist Modern linear algebra using Python instead of a textbook
Matrices in python using sympy
In this second video on the use of sympy to do calculations in linear algebra, we take a look at the Jupyter Notebook, our coding environment in python. I also show you how to construct your first matrix, as well as a few in-built matrices such as the identity matrix. Finally, I show you
From playlist Modern linear algebra using Python instead of a textbook
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
This video introduces the identity matrix and illustrates the properties of the identity matrix. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
MATH2018 Lecture 6.2 Special Matrices
We look at the properties of invertible matrices, symmetric matrices, and orthogonal matrices, and discuss some important relationships between them.
From playlist MATH2018 Engineering Mathematics 2D
David Mond: The intersection form, logarithmic vector fields, and the Severi strata..
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX In this lecture we count the degrees of freedom for the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Silke Glas: Symplectic model reduction of Hamiltonian systems on nonlinear manifolds
CONFERENCE Recorded during the meeting "Energy-Based Modeling, Simulation, and Control of Complex Constrained Multiphysical Systems" the April 19, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other
From playlist Numerical Analysis and Scientific Computing
Unitary, Symplectic, and Orthogonal Moments of Moments - Emma Bailey
Analysis - Mathematical Physics Topic: Unitary, Symplectic, and Orthogonal Moments of Moments Speaker: Emma Bailey Affiliation: University of Bristol Date: November 15, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
How to Find Periodic Orbits and Exotic Symplectic Manifolds - Mark McLean
Mark McLean Massachusetts Institute of Technology; Member, School of Mathematics October 15, 2012 I will give an introduction to symplectic geometry and Hamiltonian systems and then introduce an invariant called symplectic cohomology. This has many applications in symplectic geometry and
From playlist Mathematics
Iva Halacheva: Schubert calculus and self-dual puzzles
Abstract: Puzzles are combinatorial objects developed by Knutson and Tao for computing the expansion of the product of two Grassmannian Schubert classes. I will describe how selfdual puzzles give the restriction of a Grassmannian Schubert class to the symplectic Grassmannian in equivariant
From playlist Useful math
Lie Groups and Lie Algebras: Lesson 5 - The Classical Groups Part III
Lie Groups and Lie Algebras: Lesson 5 - The Classical Groups Part III We consider the notion of a transformation that preserves the structure of a metric and show that the set of such transformations is a group. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
A panoramic view of Mathematics Research @ICTS by Varun Thakre and Anish Mallick
ICTS In-house 2019 Organizers: Adhip Agarwala, Ganga Prasath, Rahul Kashyap, Gayathri Raman, Priyanka Maity Date and Time: 23rd April, 2019 Venue: Ramanujan Lecture Hall, ICTS Bangalore inhouse@icts.res.in An exclusive day to exchange ideas and discuss research amongst members of ICTS.
From playlist ICTS In-house 2019
In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations
Dynamics, numerical analysis and some geometry – Christian Lubich – ICM2018
Plenary Lecture 18 Dynamics, numerical analysis and some geometry Christian Lubich Abstract: Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we revi
From playlist Plenary Lectures