Linearly independence

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Let $B(i)=[v(i)~~Av(i)~~A^2v(i)~~\ldots~A^{L-1}v(i)]$ where $A$ is an $n\times n$ matrix, $v(i)$ an $n\times 1$ random vector, and $B(i)$ an $n\times L$ matrix. What are the conditions on $A$ to obtain a matrix $B=\mathbb{E}\{B^\top(i)B(i)\}$ that is invertible ($\mathbb{E}$ is the expectation operator)?