A linear space is a basic structure in incidence geometry. A linear space consists of a set of elements called points, and a set of elements called lines. Each line is a distinct subset of the points. The points in a line are said to be incident with the line. Any two lines may have no more than one point in common. Intuitively, this rule can be visualized as the property that two straight lines never intersect more than once. Linear spaces can be seen as a generalization of projective and affine planes, and more broadly, of 2- block designs, where the requirement that every block contains the same number of points is dropped and the essential structural characteristic is that 2 points are incident with exactly 1 line. The term linear space was coined by in 1964, though many results about linear spaces are much older. (Wikipedia).
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
Euclidean n Space. Norm and distance in n space.
From playlist Linear Algebra
13C Norm and Distance in Euclidean n Space
Norm and distance in Euclidean n-Space.
From playlist Linear Algebra
The formal definition of a vector space.
From playlist Linear Algebra Done Right
13F Example Problems for Euclidean n Space
Some example problems in Euclidean n-Space.
From playlist 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
Using linear algebra to solve for equation of lines and planes.
From playlist Linear Algebra
Definition of linear map. Algebraic properties of linear maps.
From playlist Linear Algebra Done Right
Geometrical Structure and the Direction of Time
Franke Program in Science and the Humanities Geometrical Structure and the Direction of Time Professors David Albert and Tim Maudlin visited Yale to give lectures and participate in discussion for an event titled "Mechanical Explanations and the Direction of Time." Tim Maudlin is Professor
From playlist Franke Program in Science and the Humanities
An Intuitive Introduction to Projective Geometry Using Linear Algebra
This is an area of math that I've wanted to talk about for a long time, especially since I have found how projective geometry can be used to formulate Euclidean, spherical, and hyperbolic geometries, and a possible (and hopefully plausible) way projective geometry (specifically the model t
From playlist Summer of Math Exposition 2 videos
Pre-recorded lecture 1: Introduction. What is Nijenhuis Geometry?
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Beyond linear algebra - Bernd Sturmfels
Bernd Sturmfels University of California, Berkeley December 10, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Bernd Sturmfels (8/28/18): Learning algebraic varieties from samples
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining polynomials. All algorithms are tested on a range of
From playlist AATRN 2018
algebraic geometry 5 Affine space and the Zariski topology
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of affine space and its Zariski topology.
From playlist Algebraic geometry I: Varieties
Seminar on Applied Geometry and Algebra (SIAM SAGA): Bernd Sturmfels
Date: Tuesday, February 9 at 11:00am EST (5:00pm CET) Speaker: Bernd Sturmfels, MPI MiS Leipzig / UC Berkeley Title: Linear Spaces of Symmetric Matrices. Abstract: Real symmetric matrices appear ubiquitously across the mathematical sciences, and so do linear spaces of such matrices. We
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)
Tropical Geometry - Lecture 6 - Structure Theorem | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Using linear algebra to solve for equations of lines and planes.
From playlist Linear Algebra
Geometry of tropical varieties with a view toward applications (Lecture 4) by Omid Amini
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)