Sparse matrix factorizations in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a sparse matrix?

A sparse matrix is a matrix mostly filled with zeros. It saves memory by only storing the non-zero values and their positions.

beginner

Why do we use sparse matrix factorizations?

We use sparse matrix factorizations to solve large systems of equations efficiently by taking advantage of the many zeros to reduce computation and memory use.

intermediate

Name two common sparse matrix factorizations available in SciPy.

LU factorization and QR factorization are two common sparse matrix factorizations in SciPy.

intermediate

What is the difference between LU and Cholesky factorization?

LU factorization breaks a matrix into lower and upper triangular matrices and works for general matrices. Cholesky factorization works only for symmetric, positive-definite matrices and breaks them into a lower triangular matrix and its transpose.

beginner

How do you perform a sparse LU factorization using SciPy?

Use the function scipy.sparse.linalg.splu() on a sparse matrix to get its LU factorization.

What does a sparse matrix mainly contain?

A Mostly zeros

B Mostly ones

C Random numbers

D Only positive numbers

Sparse matrices mainly contain zeros, which helps save memory.

Which SciPy function is used for sparse LU factorization?

A scipy.sparse.cholesky()

B scipy.linalg.lu()

C scipy.sparse.linalg.splu()

D scipy.linalg.inv()

scipy.sparse.linalg.splu() performs LU factorization on sparse matrices.

Cholesky factorization requires the matrix to be:

A Symmetric and positive-definite

B Square and invertible

C Diagonal

D Sparse only

Cholesky factorization only works on symmetric, positive-definite matrices.

Why is sparse matrix factorization faster than dense matrix factorization?

A Because it uses more memory

B Because it ignores zeros and stores less data

C Because it converts to dense first

D Because it uses random numbers

Sparse factorization is faster because it skips zeros and uses less memory.

Which factorization splits a matrix into lower and upper triangular matrices?

A Eigen decomposition

B Cholesky factorization

C QR factorization

D LU factorization

LU factorization splits a matrix into lower and upper triangular matrices.

Explain what sparse matrix factorization is and why it is useful.

Think about how zeros affect storage and computation.

Describe the difference between LU and Cholesky factorizations in sparse matrices.

Consider the matrix properties each factorization needs.