Why Do Determinants Count Trees?
Learn for free on Brilliant for a full 30 days: https://brilliant.org/AnotherRoof/ You’ll also get 20% off an annual Premium subscription. ⬣ LINKS ⬣ ⬡ PATREON: / anotherroof ⬡ CHANNEL: / anotherroof ⬡ WEBSITE: https://anotherroof.top ⬡ SUBREDDIT: / anotherroof ⬡ TWITCH: / anotherroof ⬣ ABOUT ⬣ An immensely satisfying theorem that allows us to calculate a graph's number of spanning trees using matrix determinants. ⬣ TIMESTAMPS ⬣ 00:00 - Intro 01:45 - Initial Attempts and Plan 04:02 - A Short History of Determinants 07:46 - Determinants and Permutations 12:14 - From Spanning Trees to Arborescences 17:00 - Counting Arborescences 24:08 - Final Example 27:00 - Concluding Thoughts ⬣ ANSWERS ⬣ For the "Extra Practice" matrices, we should get these determinants: 1. (the 3x3 matrix) 2 2. (the 4x4 matrix) 79 ⬣ INVESTIGATORS ⬣ Nothing for you here. Sorry! ⬣ REFERENCES ⬣ James Joseph Sylvester Memorial Address - Fabian Franklin https://www.ams.org/journals/bull/189... The collected mathematical papers of James Joseph Sylvester https://archive.org/details/collected... "The determinant | Chapter 6, Essence of linear algebra" - 3Blue1Brown • The determinant | Chapter 6, Essence of li... "Interpreting determinants in terms of area | Matrices | Precalculus | Khan Academy" - Khan Academy • Interpreting determinants in terms of area... "What is a determinant?" - Leios Labs • What is a determinant? "Why is the determinant like that?" - broke math student • Why is the determinant like that? ⬣ CREDITS ⬣ Music by Danijel Zambo, Sky Toes & Guilio Fazio
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