Theorems in algebraic geometry | Invariant theory

Gram's theorem

In mathematics, Gram's theorem states that an algebraic set in a finite-dimensional vector space invariant under some linear group can be defined by absolute invariants. (Dieudonné & Carrell , p. 31). It is named after J. P. Gram, who published it in 1874. (Wikipedia).

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What is the remainder theorem for polynomials

👉 Learn about the remainder theorem and the factor theorem. The remainder theorem states that when a polynomial is divided by a linear expression of the form (x - k), the remainder from the division is equivalent to f(k). Similarly, when a polynomial is divided by a linear expression of th

From playlist Remainder and Factor Theorem | Learn About

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What is the factor Theorem

👉 Learn about the remainder theorem and the factor theorem. The remainder theorem states that when a polynomial is divided by a linear expression of the form (x - k), the remainder from the division is equivalent to f(k). Similarly, when a polynomial is divided by a linear expression of th

From playlist Remainder and Factor Theorem | Learn About

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Use the Remainder Theorem to Determine if a Binomial is a Factor of a Polynomial

This video explains how to use the remainder theorem to determine if a binomial is a factor of a given polynomial. http://mathispower4u.com

From playlist Finding the Zeros of Polynomial Functions

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Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem

In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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Classify a polynomial then determining if it is a polynomial or not

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

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How to determine if a factor is a factor of a polynomial using factor theorem

👉 Learn about and how to apply the remainder and factor theorem. The remainder theorem states that f(a) is the remainder when the polynomial f(x) is divided by x - a. Thus, given a polynomial, f(x), which is to be divided by a linear binomial of form x - a, the remainder of the division is

From playlist Remainder and Factor Theorem

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Orthonormal Bases

Orthonormal bases. The Gram-Schmidt Procedure. Schuur's Theorem on upper-triangular matrix with respect to an orthonormal basis. The Riesz Representation Theorem.

From playlist Linear Algebra Done Right

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Using the remainder theorem to confirm if you have a zero or not

👉 Learn about and how to apply the remainder and factor theorem. The remainder theorem states that f(a) is the remainder when the polynomial f(x) is divided by x - a. Thus, given a polynomial, f(x), which is to be divided by a linear binomial of form x - a, the remainder of the division is

From playlist Remainder and Factor Theorem

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Using the remainder theorem and checking your answer with synthetic division

👉 Learn about and how to apply the remainder and factor theorem. The remainder theorem states that f(a) is the remainder when the polynomial f(x) is divided by x - a. Thus, given a polynomial, f(x), which is to be divided by a linear binomial of form x - a, the remainder of the division is

From playlist Remainder and Factor Theorem

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Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 5/5

The main topics will be the intersection theory of tautological classes on moduli space of curves, the enumeration of stable maps via Gromov-Witten theory, and the enumeration of sheaves via Donaldson-Thomas theory. I will cover a mix of classical and modern results. My goal will be, by th

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Symmetric Matrix

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

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Determining if a equation is a polynomial or not

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

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C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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Intermediate Symplectic Capacities - Alvaro Pelayo

Alvaro Pelayo Washington University; Member, School of Mathematics March 1, 2013 In 1985 Misha Gromov proved his Nonsqueezing Theorem, and hence constructed the first symplectic 1-capacity. In 1989 Helmut Hofer asked whether symplectic d-capacities exist if 1 greater than d greater than n.

From playlist Mathematics

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Oxford Linear Algebra: Spectral Theorem Proof

University of Oxford mathematician Dr Tom Crawford goes through a full proof of the Spectral Theorem. Check out ProPrep with a 30-day free trial to see how it can help you to improve your performance in STEM-based subjects: https://www.proprep.uk/info/TOM-Crawford Test your understandin

From playlist Oxford Linear Algebra

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02.10 - ISE2021 - Language Model and N-Grams - 1

Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 4: Natural Language Processing - 3 2.10 Language Model and N-Grams - 1 - How to predict a word? - N-grams - Statistical language models - Bayes Theorem Playlist: htt

From playlist ISE 2021 - Lecture 04, 05.05.2021

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Statistics - 3.2.2 Empirical Rule and Chebyshev's Theorem

We continue section 3.2 by discussing the Empirical rule used for normal data. We can determine the data values in which we can find 68% of our data, 95% of our data or 99.7% of our data. We also look at Chebyshev's Theorem which gives us similar values for non-normal data. Power Point:

From playlist Applied Statistics (Entire Course)

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How to use the remainder theorem for polynomials

👉 Learn about and how to apply the remainder and factor theorem. The remainder theorem states that f(a) is the remainder when the polynomial f(x) is divided by x - a. Thus, given a polynomial, f(x), which is to be divided by a linear binomial of form x - a, the remainder of the division is

From playlist Remainder and Factor Theorem

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Holomorphic Curves and the ADHM Vortex Equations by Aleksander Doan

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

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Algebraic set | Mathematics | Linear group | Jørgen Pedersen Gram