Skip to content

Linear Algebra

Resources:

Oreilly Text

Overview

Math is often related to AI via linear algebra.

Linear algebra:

  • Branch of continuous mathematics

  • Involves study of vector space & operations performed in vector space.

Types of Objects

The basic building blocks of matrices & tensors are the primary data structures for solving, optimizing, and approximating within an ANN.

4 fundamental types of LA objects used in AI:

  • Scalars: Singular, real numbers. Integer or floating point.

  • Vectors: 1D arrays of integers. Geometrically, they store the direction & magnitude of change from a point.

  • Matrices: 2D lists of numbers. Contain rows & columns.

  • Tensors: These store info throughout NNs that allow them to operate.

    • A tensor is a generalized matrix. They have different sizes (ranks), which measure their dimensions.

    • Tensors are 3D+ lists.

    • Tensors have a unique transitive property and form; if a tensor transforms another entity, it too must transform.

    • Can represent word embeddings, weights in a neural network, etc