List of useful Linear Algebra topics and examples of there application in FE.

[NewbietoMFEWorld]

Hello Folks, I am preparing for MFE admission for next year and I was trying to brush up my pre req math. I am seeing that linear algebra gets mentioned everywhere as being important to MFE, can some one pls list the topics in financial engineering where it is used and which specific topics I need to brush up from linear algebra perspective. I am just trying to narrow down my preparation of subset of Linear Algebra topics which will be useful for me.Thanks!!!

 

[Shantanu Kumar]

Linear Algebra is as basic as real analysis/analysis.Its hard to find their direct application.All the mathematical theories you study have somehow evolved from the combination of algebra,analysis,linear algebra and similar basic mathematical topics.
For starters you should at least have 1st level course in Linear Algebra.All kind of matrix decomposition like cholesky,QR,SVD etc have evolved from Linear Algebra. Wherever you are using Matrix and vector you are using Linear Algebra.
Bare minimum broad topics would be:
Linear Equations
Matrices
Vector Space
Matrix Decompostions

 

[vuze]

Or in addition to what Shantanu.Kumar suggests and if you feel more advanced look into how linear algebra relates to functional analysis.

 

[bigbadwolf]

Or in addition to what Shantanu.Kumar suggests and if you feel more advanced look into how linear algebra relates to functional analysis.

If by functional analysis, you mean the study of Banach and Hilbert spaces -- which are infinite-dimensional vector spaces -- that is a mistaken suggestion. For example, the spectral theorem for compact operators in Hilbert space has an altogether different and more abstract approach than the spectral theorem for self-adjoint linear operators on a finite-dimensional space. It's finite-dimensional theory the OP needs.

 

[Barny]

Is infinite dimensional stuff useless in quant finance then? All that time I've spent doing quantum mechanics..what a waste.

 

[bigbadwolf]

Is infinite dimensional stuff useless in quant finance then? All that time I've spent doing quantum mechanics..what a waste.

Not completely useless. It's handy in areas like PDEs, where it gets much of its motivation from (along with quantum field theory and von Neumann's Hilbert-space formulation of quantum mechanics) But it's definitely back-burner stuff: ars longa, vita brevis. What's needed for an MFE student is to be au fait with finite-dimensional theory -- everything upto the (f.d.) spectral theorem.

 

[boneil]

BBW what kind of math education do you have? Just wondering

Not completely useless. It's handy in areas like PDEs, where it gets much of its motivation from (along with quantum field theory and von Neumann's Hilbert-space formulation of quantum mechanics) But it's definitely back-burner stuff: ars longa, vita brevis. What's needed for an MFE student is to be au fait with finite-dimensional theory -- everything upto the (f.d.) spectral theorem.

 

[figoliuxi]

I am recently reviewing Linear Algebra for my incoming Mathematical Finance master study and I have the same question. Which parts of it are most useful and related to pursue FE? Time is limited, I have to cover those importances.

Anyway, in my review and from what I know, I guess stochastic analysis is the core of FE, in which Linear Algebra is not that important. Maybe there need to study Linear Algebra for some Numerical Analysis techniques.

 

[vuze]

If by functional analysis, you mean the study of Banach and Hilbert spaces -- which are infinite-dimensional vector spaces -- that is a mistaken suggestion. For example, the spectral theorem for compact operators in Hilbert space has an altogether different and more abstract approach than the spectral theorem for self-adjoint linear operators on a finite-dimensional space. It's finite-dimensional theory the OP needs.

You are correct. I had PDEs in mind when I posted my suggestion.