Linear Algebra

✅ Quick answer: Two vectors are orthogonal if and only if their dot product equals zero. To check orthogonality, compute

Table of Contents What is the Span of Vectors? The span of vectors is the set of all possible linear

⚡ TL;DR: The matrix trace (sum of diagonal elements) is a fundamental linear algebra operation with seven key properties —

A triangular matrix is one of the most important types of square matrices in linear algebra, characterized by having all

The determinant of matrix is a scalar value that can be computed from the elements of a square matrix. The

⚡ TL;DR: LU decomposition factors any square matrix \(A\) into \(L \cdot U\) (lower × upper triangular), enabling fast solutions

⚡ TL;DR: Eigenvectors and eigenvalues reveal the natural directions and scaling factors hidden inside any square matrix — they are

TL;DR: The rank of a matrix is the number of linearly independent rows or columns. To find it, reduce the

Vector Subtraction Vector subtraction is one of the fundamental operations you’ll use constantly in machine learning. Whether you’re calculating gradients