1. Advanced Data Structure using C++

LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110)
(C) TRANSPOSE:‐
The transpose of a m*n matrix A is an n*m matrix B (denoted as A T
) with the property bij = aji (for 0 ≤ i ≤ n‐1 and 0 ≤ j ≤ m‐1).
The transpose of a matrix A is another matrix A T (also written A′) can be created
by any one of the following equivalent actions:
• Write the rows of A as the columns of A T .
• Write the columns of A as the rows of A T .
• Reflect A by its main diagonal (which starts from the top left) to obtain A T
INTRODUCTION OF SPARSE MATRICES
A sparse matrix is a matrix that allows special techniques to take advantage of
the large number of zero elements. This definition helps to define "how many"
zeros a matrix needs in order to be "sparse." The answer is that it depends on
what the structure of the matrix is, and what you want to do with it.
Conceptually, sparsity corresponds to systems which are loosely coupled.
Consider a line of balls connected by springs from one to the next; this is a
sparse system. By contrast, if the same line of balls had springs connecting every
ball to every other ball, the system would be represented by a dense matrix.
Prepared By :­
Er. Harvinder Singh
Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 124 ‐