A Linear Algebra Primer for Financial Engineering: Covariance Matrices, Eigenvectors, OLS, and more (Financial Engineering Advanced Background Series)

This book covers linear algebra methods for financial engineering applications from a numerical point of view. The book contains many such applications, as well as pseudocodes, numerical examples, and questions often asked in interviews for quantitative positions.
Financial Applications
* The Arrow–Debreu one period market model
* One period index options arbitrage
* Covariance and correlation matrix estimation from time series data
* Ordinary least squares for implied volatility computation
* Minimum variance portfolios and maximum return portfolios
* Value at Risk and portfolio VaR
Linear Algebra Topics
* LU and Cholesky decompositions and linear solvers
* Optimal solvers for tridiagonal symmetric positive matrices
* Ordinary least squares and linear regression
* Linear Transformation Property
* Efficient cubic spline interpolation
* Multivariate normal random variables
The book is written in a similar spirit as the best selling “A Primer for the Mathematics of Financial Engineering” by the same author, and should accordingly be useful to a similarly large audience:
* Prospective students for financial engineering or mathematical finance programs will be able to self-study material that will prove very important in their future studies
* Finance practitioners will find mathematical underpinnings for many methods used in practice, furthering the ability to expand upon these methods
* Academics teaching financial engineering courses will be able to use this book as textbook, or as reference book for numerical linear algebra methods with financial applications.