10 docs tagged with "linear-algebra"

Understanding the determinant of a matrix, its geometric meaning (scaling factor), and its crucial role in checking for matrix invertibility in ML.

Understanding matrix diagonalization, its geometric meaning as a change of basis, and how it simplifies matrix computations, especially in complex systems and Markov chains.

A beginner-friendly explanation of Eigenvalues and Eigenvectors, their geometric meaning, and their critical role in dimensionality reduction (PCA) and data analysis.

Defining the inverse of a matrix, its calculation, the condition for invertibility (non-singular), and its essential role in solving linear equations in ML.

An introduction to matrices, their definition, structure (rows and columns), and their essential role in representing entire datasets and system transformations in ML.

Mastering the fundamental matrix operations: addition, subtraction, scalar multiplication, matrix transpose, and the crucial matrix multiplication used in all neural networks.

Understanding scalars, the fundamental single-number quantities in linear algebra and machine learning.

A detailed explanation of Singular Value Decomposition (SVD), why it is the most general matrix decomposition, its geometric meaning, and its critical applications in dimensionality reduction and recommender systems.

Defining tensors as generalized matrices, their ranks (order), and their crucial role in representing complex data types like images and video in Deep Learning frameworks (PyTorch, TensorFlow).

A comprehensive guide to vectors, their representation, key properties (magnitude, direction), and fundamental operations in Machine Learning.