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
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
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
69 - The Cayley-Hamilton theorem
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Rainer von Sachs: Time-frequency analysis of locally stationary Hawkes processes
Abstract : In this talk we address generalisation of stationary Hawkes processes in order to allow for a time-evolutive second-order analysis. A formal derivation of a time-frequency analysis via a time-varying Bartlett spectrum is given by introduction of the new class of locally stationa
From playlist Probability and Statistics
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
Is Memorization Compatible with Learning? by Sasha Rakhlin
Program Advances in Applied Probability II (ONLINE) ORGANIZERS: Vivek S Borkar (IIT Bombay, India), Sandeep Juneja (TIFR Mumbai, India), Kavita Ramanan (Brown University, Rhode Island), Devavrat Shah (MIT, US) and Piyush Srivastava (TIFR Mumbai, India) DATE: 04 January 2021 to 08 Januar
From playlist Advances in Applied Probability II (Online)
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
[to] Greenland's Icy Mountains No. 4 (1932)
Full title reads: "Now we continue our trip to Greenland's Icy Mountains No. 4" Introductory intertitle reads: "Along with bluff old Capt. Bartlett (who accompanied Peary to the Pole), we reach Greenland's coast and meet the hardy Eskimos." Shots from on board the schooner Morris
From playlist Amazing Explorers
Stanford Lecture: Mathematical Writing - Quotations
The class notes are available as a Stanford report, Mathematical Writing (http://www-cs-faculty.stanford.edu/~knuth/papers/cs1193.pdf), and a published book (http://www-cs-faculty.stanford.edu/~knuth/klr.html). November 9, 1987 Professor Knuth is the Professor Emeritus at Stanford Univer
From playlist Donald Knuth Lectures
Education: Why ‘energy vampires’ must be slain | Kevin Bartlett | Big Think
Education: Why ‘energy vampires’ must be slain Watch the newest video from Big Think: https://bigth.ink/NewVideo Learn skills from the world's top minds at Big Think Edge: https://bigth.ink/Edge ---------------------------------------------------------------------------------- There are
From playlist Future of learning | Big Think
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)
What's Inside The Mariana Trench?
The Mariana Trench is the deepest point on Earth, void of light with the pressure of 48 jumbo jets. Yet life finds a way to survive. Very weird life. Like crustaceans with aluminum shields or the blind, translucent snailfish, the deadliest predator in the trench and of course the sea pig,
From playlist What's Inside
Jamovi 1.8/2.0 Tutorial: Moretests Add-On Module (Episode 44)
In this Jamovi tutorial, I discuss an add-on module that simply adds a couple for statistical tests for t-tests and ANOVAs. They are assumption tests: Komolgorov-Smirnov, Anderson, and Bartlett's tests Jamovi stats: https://www.jamovi.org/ NOTE: This tutorial uses the current build of Ja
From playlist Jamovi Tutorials
Lec 17 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 17: Design of FIR digital filters Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6-008 Digital Signal Processing, 1975
Benjamin Bartlett - Walking with Dinosaurs (Music from the BBC TV Series) (1999) (Full Album)
00:00 Walking with Dinosaurs 01:13 The Ankylosaurus 02:08 Death of the Postosuchus 04:36 Survival of the Cynodonts 05:52 Torosaurus Lock Horns 08:50 Giant of the Skies 12:39 Flight of the Ornithocheirus 15:04 Deadly Nightscape 16:57 Time of the Titans 20:34 Escape of the Podlets 21:21 Jura
From playlist Brilliant Music
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
In Peary's Footsteps No 7 (1933)
North Pole. Titles read: "IN PEARY'S FOOTSTEPS - (No 7) - in company with bluff old Captain Bob Bartlett, companion to Peary when he made his dash to the Pole." "Further supplies for the Peary Monument have to be landed and this week Captain Bob carries on with hard task." M/Ss of
From playlist Amazing Explorers