A weight matrix in a computational model is defined by the expression $\mathbf{W} \in \mathbb{R}^{1024 \times 256}$. Based solely on this mathematical expression, what can be concluded about the structure of the matrix $\mathbf{W}$?

A single computational layer is designed to process input vectors. If an input vector has a dimension of 512 and is transformed by a weight matrix defined as $\mathbf{W} \in \mathbb{R}^{512 \times 128}$, what will be the dimension of the resulting output vector?

Defining a Transformation Matrix

Concatenated Weight Matrix ($\mathbf{W}_h$)