Recent content by GoodSpirit

I really thank you both! :) True Chiro, they are! I'm looking for finite-dimension spaces theory. All the best Ricardo Sousa

Hello everyone, I’m looking for very good books of advanced algebra that have a lot of information about vector spaces algebra, in particular. Would you suggest anyone? Many thanks Best regards

Hi there, Thank you for answering. Actually I found the answers in this book "Matrix Analysis and Applied Linear Algebra" I´ve been busy lately in a paper writing sorry for not answer sooner. All the best GoodSpirit.

Hi Conquest, A,B and C are rectangular matrices and there are 3 questions. I'm trying to find a function f for each case. R(X) is the range of the column space defined by the matrix X. equality is and equation or set of equations that relate variables somehow. Like this This is the...

It's pretty easy! You'll see

Hi raopeng, Could you explain a little bit more? Best regards GoodSpirit

Hello everyone, I’d like to find the following range equalities: Considering the following: A=B+C \\ A=B.C^T \\ A=[ B^T C^T ]^T I would like to find the function f for each equality above. .\\ dim( R(A) ) = f( R(B) , R(C) )\\ Considere that all matrices have compatible...

Hi mfb, Thank you for answering! :) True! it depends on something more! M is also a covariance matrix so C is related to S1 and S2. It is a good idea to make the rank M dependent of the C rank. The rank of M may be dependent of the eigen values that are shared by S1 and S2...

Hello everyone, I would like to post this problem here in this forum. Having the following block matrix: \begin{equation} M=\begin{bmatrix} S_1 &C\\ C^T &S_2\\ \end{bmatrix} \end{equation} I would like to find the function $f$ that holds rank(M)=f( rank(S1), rank(S2)). S_1 and S_2 are...

Hi tiny-tim, Thank you for answering. That´s an interesting idea but how do you do that...? It is not easy... I must say that there is more... M is a typical covariance matrix so it is symmetric and semi-positive definite. A and D are symmetric and positive semi-definite (covariance...

Hi everybody, I’m trying to compute the square root of the following squared block matrix: \begin{equation} M=\begin{bmatrix} A &B\\ C &D\\ \end{bmatrix} \end{equation} (that is M^(1/2))as function of A,B,C, D which are all square matrices. Can you help me? I sincerely...

Hello, In order to be invertible, S mustn't have zero eigen values, that is , must be positive definite or negative definite. Apart from that , that expression must work... All the best GoodSpirit

Hello everybody, I’d like to present this math problem that I’ve trying to solve… This matter is important because the covariance matrix is widely use and this leads to new interpretations of the cross covariance matrices. Considering the following covariance block matrix ...

LateX didn't work here How to present an equation here? Thank you Good Spirit

Hello, Trying to update the equation presentation. F(S,P)=tr(S-S P^T(A+PSP^T)^-1 PS) A is positive definite I've using matrix derivatives What do you think? All the best GoodSpirit