Question

In svd, the matrix a of dimension m x n can be decomposed in to a=usvt, where v is a ___________.

Answer 1

It is given that, Dimension of a matrix a is m×n, where m is the number of rows and n is number of columns.

Now, the Matrix "a" is decomposed into a = us v t,

It is also given that Matrix 'a' has m rows and n columns.

→m × n = u s v t

It means m is decomposed into u × s and n is decomposed to v × t,

For m × n to exist number of columns of 'm' i.e s, should coincide with number of rows of "n" i.e v.

Here "v" is the number of rows of "n" i.e when n is factorized into  

v × t.