Discover how to apply advanced linear algebra and its principles to derive machine learning implementations. Explore PCA, tensors, decomposition, and singular-value decomposition, as well as how to reconstruct a rectangular matrix from singular-value decomposition. The role of statistics and probability, with focus on parameter estimation and Gaussian distribution, is also covered.

Linear Algebra & Probability: Advanced Linear Algebra

discover the key concepts covered in this course

use Python libraries to implement principal component analysis with matrix multiplication

describe sparse matrix and the operations that can be performed on sparse matrix

define the concept of tensors in linear algebra and list the arithmetic operations that can be applied on tensors

implement Hadamard product on tensors using Python

describe singular-value decomposition and how to calculate it

reconstruct a rectangular matrix from single-value decomposition

recognize the characteristics of probability that are applicable in machine learning

describe probability in linear algebra and its role in machine learning

recall the types of random variables and the functions that can be used to manage random numbers in probability

describe the concept and characteristics of central limit theorem and means and recognize common usage scenarios

describe parameter estimation and distribution using Gaussian

describe binomial distribution and its characteristics

recall the arithmetic operations that can be applied on tensors, list the features of multivariate statistics that are applicable in machine learning, and implement Hadamard product on tensors using Python