1. There are many identities involving the pseudoinverse. Let m ×n . Show that 2. Show that if m ×n 3. Show that if  has orthonormal columns, then † = T . 4. If m ×n  then n ×m is a right inverse of...

1. There are many identities involving the pseudoinverse. Let

^m
×n. Show that

2. Show that if

^m
×n

3. Show that if
 has orthonormal columns, then
† =

^T.

4. If

^m
×n
 then

^n
×m
is a right inverse of
 if

<sup>m
×m

n
×m</sup>
is a left inverse of
 if
^n
×n

 Prove that if rank
† is a left inverse of

 Prove that if rank
† is a right inverse of

5. If

^m×n
 is of full rank, show that Definitions 16.3 and 16.6 for
† are equivalent.

6.

7. Prove that all solutions
 of min_x
∈R
ⁿ

₂
are of the form
† where