What are the limitations and capabilities of pseudo inverses?

[worryingchem]

Hi, I was wondering what the major advantages and disadvantages of a pseudo inverse as compared to a regular inverse are.
In class, we're usually told to the number of equations have to match the number of unknowns to find a solution. I thought that the reason for that was so we can make a square matrix using those equations and calculate the unknown from taking the inverse. But after learning pseudo inverse, you can solve for unknowns when there are more unknowns than equations. So to restate my question, is there a limitation to the pseudo inverse, then? Can it do everything a regular inverse do?

 

[RUber]

The limitation to the pseudo inverse is that it is not unique. You will have elements that are in the null space of the pseudo inverse operator.
Applications and drawbacks depend on your specific set up, but smartly applying pseudo inverses can be very useful.