Recent content by p4wp4w

I am a bit confused with your notation. Since you have used ##Q_{\bar{B}_2}## which comes out of the QR factorization as ##\bar{B}_2=Q_{\bar{B}_2}R_{m}##, and ##Q_C## in your formulation is defined as ##C=[\bar{B}_2|\textbf{v}_i|_{i=m+1:p}]=Q_CR##, shouldn't ##Q_C=Q_{\bar{B}_2}##? In that case...

Given a real-valued matrix ## \bar{B}_2=\begin{bmatrix} \bar{B}_{21}\\ \bar{B}_{22} \end{bmatrix}\in{R^{p \times m}} ##, I am looking for an orthogonal transformation matrix i.e., ##T^{-1}=T^T\in{R^{p \times p}}## that satisfies: $$ \begin{bmatrix} T_{11}^T & T_{21}^T\\ T_{12}^T...

That's a nasty mistake that I made; I think deep down, I was looking for something like SPDness of ##R## to simplify things but ##R## is not square in general.

No, it won't help really. The matrix inequality is already linear (LMI) and Schur complement in that sense will just cause a second problem that the off-diagonal terms will cause nonlinearty (later ##R## should be found by interior point method). I am expecting the answer to be in the form of a...

Hello, I want to know if there exist any result in literature that answers my question: Under which conditions on the real valued matrix ## R ## (symmetric positive definite), the first argument results in and guarantees the second one: 1) for real valued matrices ##A, B, C,## and ## D ## with...

Sure. My confusion was because of the example in my mind that s can be a very small value which then the upper bound will be also very small and as a result, physically conservatism but again mathematically correct. Thank you very much.

done!

Based on Schwartz inequality, I am trying to figure out why there should/can be the "s" variable which is the lower bound of the integration in the RHS of the following inequality: ## \left \|\int_{-s}^{0} A(t+r)Z(t+r) dr \right \|^{2} \leq s\int_{-s}^{0}\left \| A(t+r)Z(t+r) \right \|^{2} dr...