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For a linear system Au = b, if A is a square matrix in Hilbert space we can write $A \in \mathbb{R}^{H\times H}$.

However if u is time-dependent, can we write something like $u \in \mathbb{R}^{H\times T}$ where T denotes time?

I'm new to Math Stack Exchange, please forgive me if it's too simple, many thanks!

thinkvantagedu
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1 Answers1

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You can write $u \colon \mathbb{R} \to H$, since (if I understand you correctly) $u(t)$ is an $H$-valued function of $t \in\mathbb{R}$.

Hans Lundmark
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  • Thanks for your reply, for a finite element problem, does $\mathbb{R}^{H\times H}$ denote an $H\times H$ matrix? – thinkvantagedu Apr 20 '18 at 12:26
  • I don't really know what you mean by that. If you talk about a matrix, it should be with respect to some given basis for the space. If you just mean a linear operator on $H$, then one often writes $A\in L(H)$, for example. – Hans Lundmark Apr 20 '18 at 16:10