fl(A) where A is a square matrix

Question

We defined $fl(x)$ to be the function $fl:\mathbb{R} \rightarrow \mathbb R_b (t, s)$ (i.e., takes reals and outputs the float). What does $fl(A)$ mean when $A \in \mathbb R ^{n \times n} $? I assume it means the matrix $A^*$ with entries $a_{ij}^* = fl(a_{ij})$ but I want to confirm if this is common knowledge.

Answer 1

Your notation for the set of floating point numbers is certainly unique, but within the field of scientific computing and in the absence of any additional information, the default interpretation of the symbol $fl(A)$ is the floating point representation of the object $A$. It does not matter if $A$ is matrix or a scalar. From time to time, $fl(A)$ is used to represent the computed value of the object $A$. In those cases, the algorithm used to compute $fl(A)$ is clear from the context.