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I am studying "A generalization of PCA to the exponential family" (Collins et al., 2001) and I don't understand some notations.

What is the meaning of the matrix squared norm on page 6 ? Is it a frobenius norm?

If it's a matrix... what does matrix quotient (division) mean ?

If it's a scalar, is it equivalent to the following notation ?

$A^{(t)}=\frac{1}{\left \|\mathbf{V}^{(t-1)} \right \|^2}\mathbf{X}(\mathbf{V}^{(t-1)})^T$

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While $V$ is dimension $l \times d$, in that section Collins et. al. write, "First, we concentrate on the simplest case where there is just a single component so that $l = 1$." That makes $V$ just a vector and $\|V\|$ the regular 2-norm for vectors.

It doesn't matter in this case, but in my experience when texts or papers refer to the norm of a matrix, it often is the operator norm.

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