Scalars, Vectors, Matrices, and Tensors for Deep Learning
Summary
This introductory article explains the basic objects and notation of linear algebra used in machine learning and deep learning. It defines scalars, vectors, matrices, and higher-order tensors, with examples such as feature vectors, neural-network weights, image channels, and physical quantities. It also explains that matrices represent linear mappings and can encode transformations such as rotations, while tensor notation generalizes these familiar objects to higher dimensions.
The motivation is practical: linear algebra combines naturally with calculus and probability in model optimization, supports vectorized computation, and underlies many scientific Python libraries and GPU workloads. The article also points to numerical limits such as overflow and underflow, and names matrix factorizations used in applications including least squares and principal component analysis. It is a conceptual primer rather than a derivation-heavy textbook chapter; it gives no specific trading model, empirical result, or detailed treatment of the algebraic operations it introduces.
Key ideas
- Scalars, vectors, matrices, and tensors describe quantities with increasing numbers of dimensions.
- Feature vectors can represent input data, while matrices can represent neural-network weights and linear transformations.
- Linear algebra notation helps express computations in vectorized forms that can run efficiently on libraries and GPUs.
- Matrix factorizations such as LU, QR, and SVD support structured calculations in methods including least squares and PCA.
- Finite numerical representations can create overflow and underflow limits in computational applications.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.