How to solve a Matrixequation (Eigenoperatorequation) H*P = x*P with P = unknown matrix und x = unknown factor?

I need to solve a Matrixequation of the Form H*P = x*P where H is a wellknown Matrix and P is an unknown one with the unknown factor x. Can I use solve? And if yes how? (First try with solve did not work like I expected it) Thanks for help!

[Torsten]

Is x just a factor or a diagonal matrix ?

Is H symmetric ?

Best wishes

Torsten.