Since we're now exploring matrices and matrix multiplication, the question arises is there some matrix that has the same propertyįor matrix multiplication? To make that a little bit more concrete, is there some matrix I, and let me bold it as bestĪs I can in my handwriting, is there some matrix I that Regular multiplication or scalar multiplication, it has this identity property. And you could view it as 1, when you're thinking about Saying one of this thing is just going to be that 1 times some number isĮqual to that number again, and that makes intuitive sense. Learned multiplication many, many, many years ago, you got exposed to the But if you could provide any insight that would be extremely helpful. I know I have to look at the ranks of a matrix before trying to understand this, I will do so. I understand this is highly specialised, as in applied to a different concept however I am totally lost. What is a residual maker/annihilator matrix? What P represents? (PY is called a projection matrix) The apostrophe being 'prime' or transpose However, I do not get the relation when he has used the construction of an error term in the classical linear regression model to get:Įhat = Y - Yhat = Y - XBetahat = Y - X (X'X) ^-1 (X')Y = Y - PY product of a matrix multiplied by itself is the matrix itself. I know it's different to identity matrices but from what I have read about idempotent matrices, e.g. Hi, I am studying for a Masters in Economics and in Econometrics we use some math where the lecturer mentioned 'idempotent matrices'.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |