Matrix computations for deep learning

Matrix Computations for Deep Learning

Modern Artificial Intelligence is powered by data, algorithms, and computation. Yet beneath every neural network, convolutional layer, transformer architecture, and optimization algorithm lies a common mathematical foundation: matrix and tensor computations.

Whether training a deep neural network, compressing a model using Singular Value Decomposition (SVD), implementing convolutional operations in computer vision, or scaling machine learning systems across GPUs and distributed environments, matrix computations form the computational engine that drives modern AI.

Matrix Computations for Deep Learning: Foundations of SVD, Tensor Operations, and CNNs provides a comprehensive exploration of the mathematical structures, computational techniques, and practical implementations that enable contemporary deep learning systems.

Unlike traditional linear algebra textbooks that focus primarily on abstract theory, this book bridges mathematics and Artificial Intelligence by showing how matrix methods directly power modern neural networks, computer vision systems, optimization algorithms, and large-scale machine learning architectures.

Readers will explore:

• Foundations of Linear Algebra for Deep Learning

• Matrix Operations and Numerical Computation

• Vector Spaces, Norms, and Stability Analysis

• Singular Value Decomposition (SVD)

• QR and LU Factorizations

• Eigenvalue Methods and Spectral Techniques

• Tensor Algebra and Tensor Factorizations

• Tensor Operations in Deep Learning Frameworks

• GPU-Accelerated Matrix Computations

• Convolutional Neural Networks (CNNs)

• Matrix Representations of Convolution Operations

• Backpropagation through Matrix and Tensor Calculations

• Dimensionality Reduction Techniques

• Computer Vision Applications

• Large-Scale Distributed Matrix Computations

• Practical Implementations with NumPy, SciPy, PyTorch, and TensorFlow

The book combines mathematical rigor, computational intuition, algorithmic analysis, and hands-on implementation to help readers understand not only how deep learning systems operate, but why matrix computations are fundamental to their success.

By connecting theory, implementation, and real-world AI applications, this book empowers readers to move beyond treating neural networks as black boxes and develop a deeper understanding of the mathematical machinery behind modern intelligent systems.

• BCA, MCA, B.Tech, M.Tech and Computer Science Students

• Artificial Intelligence and Machine Learning Learners

• Deep Learning Engineers

• Computer Vision Researchers

• Data Scientists and AI Practitioners

• Graduate Students and PhD Scholars

• Researchers in Computational Mathematics

• Professionals working with Neural Networks and Large-Scale AI Systems

✔ Connects linear algebra directly with deep learning applications

✔ Covers both matrix and tensor computations in a unified framework

✔ Explains CNN operations through matrix representations

✔ Includes practical Python implementations using industry-standard frameworks

✔ Bridges mathematical theory, computational efficiency, and AI applications

✔ Covers emerging topics such as tensor compression and quantum-inspired computation

This book serves as both an academic textbook and a professional reference for anyone seeking to master the mathematical foundations of modern deep learning systems.