# InfoCoBuild

### 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (Spring 2018, MIT OCW). Instructor: Prof. Gilbert Strang. Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization-and above all a full explanation of deep learning. (from ocw.mit.edu)

 Introduction

 Lecture 01 - The Column Space of A Contains All Vectors Ax Lecture 02 - Multiplying and Factoring Matrices Lecture 03 - Orthogonal Columns in Q Give QTQ = I Lecture 04 - Eigenvalues and Eigenvectors Lecture 05 - Positive Definite and Semidefinite Matrices Lecture 06 - Singular Value Decomposition (SVD) Lecture 07 - Eckart-Young: The Closest Rank k Matrix to A Lecture 08 - Norms of Vectors and Matrices Lecture 09 - Four Ways to Solve Least Squares Problems Lecture 10 - Survey of Difficulties with Ax = b Lecture 11 - Minimizing ∥X∥ Subject to Ax = b Lecture 12 - Computing Eigenvalues and Singular Values Lecture 13 - Randomized Matrix Multiplication Lecture 14 - Low Rank Changes in A and its Inverse Lecture 15 - Matrices A(t) Depending on t, Derivative = dA/dt Lecture 16 - Derivatives of Inverse and Singular Values Lecture 17 - Rapidly Decreasing Singular Values Lecture 18 - Counting Parameters in SVD, LU, QR, Saddle Points Lecture 19 - Saddle Points (cont.), Maxmin Principle Lecture 20 - Definitions and Inequalities Lecture 21 - Minimizing a Function Step by Step Lecture 22 - Gradient Descent: Downhill to a Minimum Lecture 23 - Accelerating Gradient Descent (Use Momentum) Lecture 24 - Linear Programming and Two-Person Games Lecture 25 - Stochastic Gradient Descent Lecture 26 - Structure of Neural Nets for Deep Learning Lecture 27 - Backpropagation: Find Partial Derivatives Lecture 28 Lecture 29 Lecture 30 - Completing a Rank-One Matrix, Circulants Lecture 31 - Eigenvectors of Circulant Matrices: Fourier Matrix Lecture 32 - ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule Lecture 33 - Neural Nets and the Learning Function Lecture 34 - Distance Matrices, Procrustes Problem Lecture 35 - Finding Clusters in Graphs Lecture 36 - Alan Edelman and Julia Language

 References 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning Instructor: Prof. Gilbert Strang. Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks.