# Applications of the LU factorization in computer science [closed]

I have been searching for the applications of the LU factorization/decomposition in computer science. From Wikipedia, I have found some of the applications, but these don't seem to be relevant to computer science.

Applications I found are

• Solving linear equations
• Inverting a matrix
• Computing the determinant

Is there any application of LU factorization/decomposition in computer science?

• Linear algebra is very relevant in computer science. As an example, PCA and LDA are standard techniques for analyzing data. – Yuval Filmus Apr 5 '18 at 9:05
• @YuvalFilmus what do u mean by PCA and LDA? i am looking for the applications of lu factorization in computer sciences – JAMSHAID Apr 5 '18 at 9:09
• Use your web searching skills to figure out what these things are (the acronyms stand for Principal Component Analysis and Linear Discriminant Analysis, I believe). These are examples of applications of linear algebra in computer science. LU factorization is a basic technique in numerical linear algebra. – Yuval Filmus Apr 5 '18 at 9:15
• is LU Factorization related to LDA & PCA? – JAMSHAID Apr 5 '18 at 9:17
• Here is a relevant quote from Wikipedia: "Computers usually solve square systems of linear equations using the LU decomposition, and it is also a key step when inverting a matrix, or computing the determinant of a matrix." PCA involves singular value decomposition, which in turn involves another QR decomposition. But LDA involves inverting a matrix. – Yuval Filmus Apr 5 '18 at 9:22

## 1 Answer

LU decomposition is a basic technique in numerical linear algebra, which is "numerical analysis for linear algebra", or (roughly speaking) the study of numerical algorithms for matrices. Numerical linear algebra has many applications, since many numerical algorithms reduce to linear algebra, which is at the heart of multivariate calculus. You can find a list of areas of application on the Wikipedia article.