# Expected Value of Matrix Quadratic Forms with Wishart distributed Random Matrices

arXiv: https://arxiv.org/abs/2212.01412 · HTML: https://mlsanity.com/paper/2212.01412/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2022.

## Built on by (most cited first, 1 of 1)

- [Fine-Tuning Without Forgetting In-Context Learning: A Theoretical Analysis of Linear Attention Models](https://mlsanity.com/paper/2602.23197/) (2026)

## Abstract (arXiv)

To explore the limits of a stochastic gradient method, it may be useful to consider an example consisting of an infinite number of quadratic functions. In this context, it is appropriate to determine the expected value and the covariance matrix of the stochastic noise, i.e. the difference of the true gradient and the approximated gradient generated from a finite sample. When specifying the covariance matrix, the expected value of a quadratic form QBQ is needed, where Q is a Wishart distributed random matrix and B is an arbitrary fixed symmetric matrix. After deriving an expression for E(QBQ) and considering some special cases, a numerical example is used to show how these results can support the comparison of two stochastic methods.