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Explore All of Linear Algebra in One Video (Full Course) with 8,112 views, 215 likes, and 13 comments. Experience the impact of this video content that has captured audience attention.

Every idea in a first course on linear algebra, built one picture at a time, in one video. Ten chapters, following Gilbert Strang's Introduction to Linear Algebra (6th ed.) from vectors to the SVD and machine learning. You'll learn: • why Ax = b is a question about the columns of A, and how elimination answers it (A = LU) • the four fundamental subspaces, rank, and the dimensions that tie them together • projections and least squares, Gram-Schmidt and A = QR, and the pseudoinverse • determinants as volumes, eigenvalues and diagonalization, the spectral theorem • the singular value decomposition, PCA and the best low-rank approximation • linear transformations, gradient descent, Lagrange multipliers, linear programming, neural networks CHAPTERS 0:00 Chapter 1 · Vectors and Matrices 3:04 1.1 Vectors and linear combinations 10:58 1.2 Dot products, lengths and angles 19:31 1.3 Matrices and their column spaces 24:40 1.4 Matrix multiplication, AB and CR 31:18 Chapter 2 · Solving Ax = b 34:19 2.1 Row and column pictures 41:11 2.2 Elimination matrices 46:17 2.3 Gauss–Jordan and Turing's prediction 52:40 2.4 Permutations and partial pivoting 58:56 2.5 Derivatives from differences 1:05:47 Chapter 3 · The Four Fundamental Subspaces 1:09:47 3.1 Vector spaces and subspaces 1:15:22 3.2 The nullspace by elimination: A = CR 1:21:03 3.3 The complete solution to Ax = b 1:25:55 3.4 Independence, basis and dimension 1:32:05 3.5 Dimensions of the four subspaces 1:40:29 Chapter 4 · Orthogonality 1:43:19 4.1 Orthogonal vectors and the Pythagorean theorem 1:49:17 4.2 Projection onto a line 1:56:40 4.3 Least squares: fitting a line 2:03:46 4.4 Orthonormal columns and orthogonal matrices 2:11:35 4.5 The pseudoinverse 2:17:23 Chapter 5 · Determinants 2:19:33 5.1 What ad − bc means 2:27:12 5.2 Three rules define the determinant 2:36:04 5.3 Areas from corners 2:41:35 Chapter 6 · Eigenvalues and Eigenvectors 2:44:08 6.1 Vectors that keep their direction 2:52:57 6.2 Diagonalizing a matrix: A = XΛX⁻¹ 3:04:44 6.3 Symmetric matrices and the spectral theorem 3:12:07 6.4 Complex eigenvalues 3:19:40 6.5 Differential equations: du/dt = Au 3:27:58 Chapter 7 · The Singular Value Decomposition 3:30:09 7.1 Two sets of singular vectors 3:42:50 7.2 Flags, rank and images 3:46:40 7.3 Eckart–Young: the best low-rank approximation 3:55:44 Chapter 8 · Linear Transformations 3:58:33 8.1 What makes a transformation linear 4:06:58 8.2 The matrix of a linear transformation 4:16:46 8.3 Jordan form 4:26:39 Chapter 9 · Linear Algebra in Optimization 4:28:51 9.1 Landscapes: gradient, Hessian, saddle points 4:39:14 9.2 Stochastic gradient descent 4:45:30 9.3 Minimum norms: why L1 gives sparse answers 4:52:05 9.4 Linear programming: the diet problem 5:01:52 Chapter 10 · Learning from Data 5:04:26 10.1 Learning from examples 5:15:37 10.2 Experiments: the playground 5:21:08 10.3 Mean and variance 📘 Companion to Gilbert Strang, Introduction to Linear Algebra, 6th ed. (Wellesley-Cambridge Press, 2023). Not affiliated with the author or publisher; the examples, numbers and animations are original. 🎙 Narration: Kia Keng's own voice, cloned with Qwen3-TTS from real recordings. 🎵 Music: original ambient pad (procedurally generated). 🖼 Portraits (61, Wikimedia Commons, author and licence shown on screen with each image): Adrien-Marie Legendre, Alan Turing, Andrey Markov, Arthur Cayley, August Ferdinand Möbius, Augustin-Louis Cauchy, Camille Jordan, Carl Eckart, Carl Friedrich Gauss, Charles Hermite, David Hilbert, David Rumelhart, E. H. Moore, Erhard Schmidt, Eugenio Beltrami, Fibonacci, Francis Galton, Frank Rosenblatt, Franz Xaver von Zach, Gabriel Cramer, Gene H. Golub, Geoffrey Hinton, George Dantzig, George Pólya, Gilbert Strang, Giuseppe Peano, Giuseppe Piazzi, Gottfried Wilhelm Leibniz, Gustav Kirchhoff, Heinrich Wilhelm Matthias Olbers, Hermann Grassmann, Hermann Schwarz, Hero of Alexandria, Isaac Newton, Issai Schur, Jacques Philippe Marie Binet, Jakob Steiner, James Joseph Sylvester, Jerzy Neyman, John von Neumann, Joseph Fourier, Joseph-Louis Lagrange, Josiah Willard Gibbs, Julien-Léopold Boilly, Jørgen Pedersen Gram, Larry Page, Leonhard Euler, Lewis Carroll, Louis Legendre, Marvin Minsky, Otto Hesse, Pafnuty Chebyshev, Pierre-Simon Laplace, Queen Victoria, Roger Penrose, Seki Takakazu, Sergey Brin, Seymour Papert, Viktor Bunyakovsky, Volker Strassen, William Kahan. 🔔 Subscribe: https://www.youtube.com/@KiaKengSTEM?sub_confirmation=1 #LinearAlgebra #Math #MachineLearning

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