Problem Description Consider a matrix A of size R\"dxnd, where each non-overlapp

Question

Problem Description Consider a matrix A of size R"dxnd, where each non-overlapping d x d block of the matrix, Dij, is a diagonal matrix. So the matrix consists of n2 such blocks. An example of such a matrix is shown below: D21 D22 D2sD2n Construct an efficient data structure to represent such matrices and device algorithms to perform matrix operations, such as matrix multiplications and matrix inverse, on the data structure you designed. Provide a technical write-up of your solution along with associated code implementing your solution.

Explanation / Answer

For this the best DataStructure will be Sparse Arrays/Matrix (2-Dimensional Sparse Arrays/Matrix) with equal number of rows and columns would be best .ie Square 2D Sparse Array would be ideal since we will be storing rows and columns in it.

Here we would go for Sparse Matrix as in Diagonal Matrix the main diagonal elements will be non zero, but all other elements except the main diagonal will be 0. So in such a case Sparse Array will be an efficient Data Structure for storage because it saves lot of memory especially when most of array elements are 0.

kind of knowledge I need to know to solve this question:-

Please let me know in case of any clarifications required. Thanks!

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