Question
Consider the 10x10 matrix M defined by this file m10x10.mat: 10 10 2 1 0 0 0 0 0 0 0 0 1 2 1
Consider the 10x10 matrix M defined by this file "m10x10.mat":
10 10
2 1 0 0 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0
0 1 2 1 0 0 0 0 0 0
0 0 1 2 1 0 0 0 0 0
0 0 0 1 2 1 0 0 0 0
0 0 0 0 1 2 1 0 0 0
0 0 0 0 0 1 2 1 0 0
0 0 0 0 0 0 1 2 1 0
0 0 0 0 0 0 0 1 2 1
0 0 0 0 0 0 0 0 1 2
Note: This matrix is symmetric, making it "sparse" in the sense that most entries are zero.
Consider also the dimension 10 vector V defined by this file "v10.vec": 10 0 0 0 0 1 1 0 0 0 0 Compute the following items:
The vector W = MV
The sparse matrix representation m of M
The sparse vector representation v of V
The sparse vector representation w of W
The sparse product x = mv
Then verify that the sparse vectors w and x are equal.
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