1. Numerical Linear Algebra

Matrix Basics — Quiz

Test your understanding of matrix basics with 5 practice questions.

Practice Questions

Question 1

Which storage format is most memory-efficient for storing a dense banded matrix with bandwidth $k$ (i.e., nonzeros confined to the main diagonal and $k$ super/sub-diagonals)?

Question 2

How many elements are stored when an $n\times n$ symmetric matrix is saved in upper‐triangular packed storage?

Question 3

Consider a $10000\times10000$ sparse matrix with $0.1\\%$ nonzero entries. Approximately how many times less memory (full/CSR) does CSR storage use compared to full dense storage? Assume 8‐byte values, 4‐byte column indices, and 4‐byte row pointers.

Question 4

In block matrix multiplication, choosing a block size that fits completely in L1 cache primarily improves performance by:

Question 5

Given a double‐precision $m\times n$ array $A$ stored in row‐major order, what is the address expression for element $A[i][j]$ (zero‐based indices)?