(22) Let A be a 100 x 90 matrix, representing an image with 9000 pixels. How many numbers do we need to store for a truncated singular value decompo- sition (TSVD) A = Ak with k…

Question

asked Jan 23, 2020 30.3k views

1 Answer

Nash · Answer 1 · 2020-01-28T00:46:23+0000

Answer:

The correct option is c.

Explanation:

Let A be a 100 x 90 matrix.

The order of a matrix is m x n, where, m is number of rows and n is number of columns.

m=100

n=90

It is given that for a truncated singular value decompo- sition (TSVD)
$A\approx A_k$ with k=10.

The formula for the number of numbers do we need to store for a truncated singular value decompo- sition (TSVD)
$A\approx A_k$ is

N=k(m+n+1)

Substitute k=10, m=100 and n=90 in the above formula.

N=10(100+90+1)

N=10(191)

N=1910

The numbers that are needed to store for a truncated singular value decompo- sition (TSVD) is 1910.

Therefore the correct option is c.