Pseudo inverse

[magical light]

A = 52 30 8 2
43 36 7 1
51 32 10 2
65 21 15 2
64 22 20 1

How to find Pseudo inverse of A. (A^T*A)^-1*A^T. Is this the right formula to calculate the inverse?

Is it like :
A^T A
52 43 51 65 64 52 30 8 2
30 36 32 21 22 43 36 7 1 and then inverse of A^T*A ? which is then multiplied with A^T
8 7 10 15 20 * 51 32 10 2
2 1 2 2 1 65 21 15 2
64 22 20 1

I would be very grateful if you can provide me with a detailed solution.


Thanking you all for your replies.

 

[Deleted member 4993]

A = 52 30 8 2
43 36 7 1
51 32 10 2
65 21 15 2
64 22 20 1

How to find Pseudo inverse of A. (A^T*A)^-1*A^T. Is this the right formula to calculate the inverse?

Is it like :
A^T A
52 43 51 65 64 52 30 8 2
30 36 32 21 22 43 36 7 1 and then inverse of A^T*A ? which is then multiplied with A^T
8 7 10 15 20 * 51 32 10 2
2 1 2 2 1 65 21 15 2
64 22 20 1

I would be very grateful if you can provide me with a detailed solution.


Thanking you all for your replies.

There are on-line psuedo-inverse calculators that you can use:

http://comnuan.com/cmnn0100f/

 

[magical light]

For inverse matrix should the number of rows and columns be equal? For Eg: 5*5, 3*3 matrices.

In my case A is 4x5 matrix. Does this mean that no inverse exist? Kindly clarify my doubt. I followed the link given in the previous post but couldn't really understand it.

Thanking you for your time and replies.

 

[Deleted member 4993]

For inverse matrix should the number of rows and columns be equal? For Eg: 5*5, 3*3 matrices.

In my case A is 4x5 matrix. Does this mean that no inverse exist? Kindly clarify my doubt. I followed the link given in the previous post but couldn't really understand it.

Thanking you for your time and replies.

What does your textbook say?

Did you do a google search on the topic?

From Wikipedia:

"In mathematics, and in particular linear algebra, a pseudoinverse A⁺ of a matrix A is a generalization of the inverse matrix.^[1] The most widely known type of matrix pseudoinverse is the Moore–Penrose pseudoinverse, which was independently described by E. H. Moore^[2] in 1920, Arne Bjerhammar^[3] in 1951 and Roger Penrose^[4] in 1955. Earlier, Fredholm had introduced the concept of a pseudoinverse of integral operators in 1903. When referring to a matrix, the term pseudoinverse, without further specification, is often used to indicate the Moore–Penrose pseudoinverse. The term generalized inverse is sometimes used as a synonym for pseudoinverse.

a matrix

,

is a generalized (pseudo) inverse of

if it satisfies the condition

.