Linear Algebra for AI
Linear algebra is the backbone of AI and machine learning. Neural networks, image processing, and data transformations all rely heavily on linear algebra operations.
Why it matters: Every neural network layer is essentially a matrix multiplication. Understanding linear algebra helps you understand how AI models work internally.
Core Concepts
Scalar
A single number.
Used for: learning rates, temperatures, single values
Vector
An ordered array of numbers.
Used for: embeddings, features, activations
Matrix
A 2D array of numbers.
[3, 4]]
Used for: weights, images, transformations
Tensor
A multi-dimensional array.
[[5,6],[7,8]]]
Used for: batches of images, video, 3D data
Matrix Operations
Matrix Multiplication
The most important operation in neural networks. Each layer performs matrix multiplication.
Neural Network Connection: When data flows through a layer, it's multiplied by the weight matrix: output = input × weights + bias
Transpose
Flipping a matrix over its diagonal. Rows become columns and vice versa.
Advanced Concepts
Eigenvalues & Eigenvectors
Special vectors that only get scaled (not rotated) when a matrix is applied to them.
where v is eigenvector, λ is eigenvalue
Used in: PCA, spectral clustering, graph analysis
Singular Value Decomposition (SVD)
Factorizes a matrix into three matrices: A = U Σ V^T
Used in: dimensionality reduction, recommender systems, image compression