21.15.3. Sparse Matrices

Try these first

1. 1.

   Define a sparse matrix.

   Hint

   Think about the ratio of non-zero to zero elements.

2. 2.

   What is one application of sparse matrices?

   Hint

   Consider engineering simulations.

3. 3.

   What defines a sparse matrix?

   • A matrix with all non-zero elements
   • A matrix with a high ratio of zero elements
   • A matrix that can be only square
   • A matrix whose dimensions are equal

   Hint

   Consider the balance between zero and non-zero values.

4. 4.

   True or False: All matrices are sparse matrices.

   • True
   • False

   Hint

   Reflect on the definition we discussed.

5. 5.

   You have a large matrix from finite element analysis with only 12 non-zero values out of 100 elements. How would you convert this to a sparse matrix representation?

   Hint

   Think about what it means to store only what's necessary.

6. 6.

   Analyze a scenario where using a dense matrix for a problem caused inefficiencies. How would sparse matrices solve these pitfalls?

   Hint

   Consider the difference between filling a balloon and only keeping the essential air!