linear algebra notation and regression models

Hi everybody,

I am new here; hope that I am posting in the right forum.

What does the expression

0.5 lb'Pb

mean? .... where b is a vector, P is a matrix and l is a skalar. I don't know what b' means.

It's the penalty term from penalized maximum likelihood estimation in regression analysis. b is the vector of regression coefficients, l is an overal penalty factor, and the matrix P is used to scale penalties on individual coefficients bi, e.g. by their standard deviations. However, I don't understand why you'd need a matrix for the latter; why not simply define a vector of individual scales. In fact all examples that I saw so far used a diagonal matrix.

Thanks a lot for help !!

monalisa (biologist, learning advanced statistics)