I have a question regarding definition for matrix valued function. Suppose $f:\mathbb{R}^q \to \mathbb{R}^q \times \mathbb{R}^d$, which is a matrix valued function. Then what does it mean by $f$ is continuous differentiable? Where can I find reference for this kind of calculus material?
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Do you know multivariable calculus? Do you know what it means for a function $f : \mathbb{R}^q \to \mathbb{R}^m$ to be continuous, to be differentiable, and to be continuously differentiable? If so, set $m=q+d$… if not, look up any multivariable calculus book. – Lee Mosher Aug 22 '15 at 15:00
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Thanks. So you are saying we should vectorize the matrix as a long vector? I know multivariable but single valued function, but not quite familiar with the vector valued function. – Sean Aug 22 '15 at 15:10
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@Sean A matrix valued function would have codomain $\mathbb R^{n\times m} \simeq \mathbb R^{n\cdot m}$. Your codomain just consists of pairs of vectors, one from $\mathbb R^q$ and one from $\mathbb R^d$. – AlexR Aug 22 '15 at 15:28