In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley. It states that for every positive integer , the number of trees on labeled vertices is . The formula equivalently counts the number of spanning trees of a complete graph with labeled vertices (sequence in the OEIS). (Wikipedia).
Cayley-Hamilton Theorem Example 2
Matrix Theory: Let A be the 3x3 matrix A = [1 2 2 / 2 0 1 / 1 3 4] with entries in the field Z/5. We verify the Cayley-Hamilton Theorem for A and compute the inverse of I + A using a geometric power series.
From playlist Matrix Theory
Cayley-Hamilton Theorem: Example 1
Matrix Theory: We verify the Cayley-Hamilton Theorem for the real 3x3 matrix A = [ / / ]. Then we use CHT to find the inverse of A^2 + I.
From playlist Matrix Theory
I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.
From playlist Differential Equations
In this video I show you how to prove Cayley's theorem, which states that every group is isomorphic to a permutation group. This video is a bit long because I take the time to revisit all the concepts required in the proof. these include isomorphisms, injective, surjective, and bijective
From playlist Abstract algebra
Proof that Cayley table row and column entries are unique and complete
In this video I show a proof of why all the row and column entries in a Cayley table are unique and why all of the elements in the group appear in each row and column. This proof goes a long way towards proving Cayley's theorem.
From playlist Abstract algebra
From playlist Complex Analysis Made Simple
Cayley-Hamilton Theorem: General Case
Matrix Theory: We state and prove the Cayley-Hamilton Theorem over a general field F. That is, we show each square matrix with entries in F satisfies its characteristic polynomial. We consider the special cases of diagonal and companion matrices before giving the proof.
From playlist Matrix Theory
Inverse of a Matrix Using the Cayley-Hamilton Theorem
Matrix Theory: Suppose a 2 x 2 real matrix has characteristic polynomial p(t) = t^2 - 2t + 1. Find a formula for A^{-1} in terms of A and I. Verify the formula for A = [1 2\ 0 1].
From playlist Matrix Theory
Proof of the famous Cauchy’s integral formula, which is *the* quintessential theorem that makes complex analysis work! For example, from this you can deduce Liouville’s Theorem which says that a bounded holomorphic function must be constant. The proof itself is very neat and analysis-y Enj
From playlist Complex Analysis
C36 Example problem solving a Cauchy Euler equation
An example problem of a homogeneous, Cauchy-Euler equation, with constant coefficients.
From playlist Differential Equations
Tropical Geometry - Lecture 8 - Surfaces | 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
The Cayley Expansion (feat. David Eisenbud) - Objectivity 174
David Eisenbud joins us at The Royal Society to look at the work of one of his all time favourite mathematicians. More links below ↓↓↓ Featuring David Eisenbud speaking with Brady and Keith Moore. Subscribe to Objectivity: http://bit.ly/Objectivity_Sub Check out David on Numberphile: h
From playlist David Eisenbud on Numberphile
Jonathan Novak : Monotone Hurwitz numbers and the HCIZ integral
Recording during the thematic meeting : "Pre-School on Combinatorics and Interactions" the January 13, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Combinatorics
Cayley-Hamilton Theorem In this video, I state and prove one of the most important theorems in linear algebra: The Cayley-Hamilton Theorem. This theorem allows us to calculate some matrix equations from scratch, and intuitively says that A must satisfy its characteristic polynomial. This
From playlist Diagonalization
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms
Visual Group Theory, Lecture 4.1: Homomorphisms and isomorphisms A homomoprhism is function f between groups with the key property that f(ab)=f(a)f(b) holds for all elements, and an isomorphism is a bijective homomorphism. In this lecture, we use examples, Cayley diagrams, and multiplicat
From playlist Visual Group Theory
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3)
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3) In this video lesson we construct the Lie group elements of SO(3) starting from the defining property of SO(3) and the Lie algebra of so(3). To do this we review the Caley-Hamilton theorem that a square matrix satisfies its own cha
From playlist Lie Groups and Lie Algebras
Graph Theory: 40. Cayley's Formula and Prufer Seqences part 1/2
In this video we show how Cayley's formula (for the number of labelled trees) can be proved using Prufer sequences. An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: http://youtu.be/utfW-xsDp3Y (41. Cayley's Formula and Prufer Seqences part 2/2) https://ww
From playlist Graph Theory part-7
Find all Points for which the Cauchy Riemann Equations Hold
Find all Points for which the Cauchy Riemann Equations Hold Nice example of using the Cauchy Riemann Equations from complex variables.
From playlist Complex Analysis
Graph Theory: 41. Cayley's Formula and Prufer Seqences part 2/2
In this video we show how Cayley's formula (for the number of labelled trees) can be proved using Prufer sequences. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: http://youtu.be/Ve447EOW8ww (40. Cayley's Formula and Prufer Seqences part-1) https://ww
From playlist Graph Theory part-7