Expressing an SPD matrix A = sI + B

[rtaylor]

I would like to express an SPD matrix A as:

 

A = sI + B

 

where B is also SPD, or alternatively as:

 

 

A = I + B

 

what constraints need to be imposed on B?

Please let me know if this question is mot appropriate for this forum.

 

thanks,

 

Russ

[D H]

This looks a bit too much like homework, so all I am going to do is give a hint.

 

Let A=sI+B. Then if x is an eigenvector of B it is an eigenvector of A, and vice versa (you will need to prove this).

[DrRocket]

This looks a bit too much like homework, so all I am going to do is give a hint.

 

Let A=sI+B. Then if x is an eigenvector of B it is an eigenvector of A, and vice versa (you will need to prove this).

 

 

Hint #2 : If A is an SPD think abou the simplest form in which it can be expressed by a suitable choice of basis.