# Matrix Decomposition and Applications

arXiv: https://arxiv.org/abs/2201.00145 · HTML: https://mlsanity.com/paper/2201.00145/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jan 2022.

## Built on by (most cited first, 14 of 14)

- [Flexible and Hierarchical Prior for Bayesian Nonnegative Matrix Factorization](https://mlsanity.com/paper/2205.11025/) (2022)
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- [Bayesian Low-Rank Interpolative Decomposition for Complex Datasets](https://mlsanity.com/paper/2205.14825/) (2022)
- [Autoencoding Conditional GAN for Portfolio Allocation Diversification](https://mlsanity.com/paper/2207.05701/) (2022)
- [AdaSmooth: An Adaptive Learning Rate Method based on Effective Ratio](https://mlsanity.com/paper/2204.00825/) (2022)
- [Comparative Study of Inference Methods for Interpolative Decomposition](https://mlsanity.com/paper/2206.14542/) (2022)
- [Robust Bayesian Nonnegative Matrix Factorization with Implicit Regularizers](https://mlsanity.com/paper/2208.10053/) (2022)
- [A Hybrid Approach on Conditional GAN for Portfolio Analysis](https://mlsanity.com/paper/2208.07159/) (2022)
- [Feature Selection via the Intervened Interpolative Decomposition and its Application in Diversifying Quantitative Strategies](https://mlsanity.com/paper/2209.14532/) (2022)
- [Efficient State Space Model via Fast Tensor Convolution and Block Diagonalization](https://mlsanity.com/paper/2402.15290/) (2024)
- [Large Language Model Compression via the Nested Activation-Aware Decomposition](https://mlsanity.com/paper/2503.17101/) (2025)
- [Generative Models: Principles, Architectures, and Applications](https://mlsanity.com/paper/2608.08101/) (2026)

## Abstract (arXiv)

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the backpropagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition, given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.