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What’s New: KVR Audio – [New X86] – x86. v1.3.0. Free. Update Today.Q:

Why does the “–” in a tcl command prompt show as one of its options?

When I type in tclsh command prompt the following command
list x 10 —
I am expecting to get:
../list.tcl x 10

but I am getting
../list.tcl x 10 —

I do know that when I run the above code as a script, it works fine, but I am curious why it works as such.


It is for historical reasons. The — was a common way to specify multiple options in interactive (referring to the console) programs.
Most of the time, interactive Tcl programs just ignore the — (or any options following it) entirely, so it doesn’t affect the behavior of the program in any way.
However, there are two things to consider. First, some Tcl programs will return a value as if the program was successful, but still leave some bytes of the original input buffer available for the next caller. This value is likely to

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Associative properties of tensor product

Consider a tensor product of vector spaces $V_1\otimes V_2$, where $V_1$ is finite dimensional, and so is $V_2$.
Consider also a mapping $F: V_1 \to V_2$ (an endomorphism of the vector space $V_1$, or of $V_2$ for that matter, doesn’t matter which). Let $F=\sum_{i=1}^n\lambda_i E_i$, where $E_i \in \text{End}(V_2)$, and $\lambda_i$ are complex numbers.
Now, let $V=V_1\otimes V_2$, and for each vector $v \in V_1$, define a linear operator $F_{v}:V_2 \to V_2$ by:
$$ F_{v}(w) = F(v\otimes w), \ \ \forall v \in V_1 \ \ \ \text{and} \ \ \ \forall w \in V_2. \ \ \ (1) $$
Then, it is easy to check that this defines a linear endomorphism of $V_2$, for the action on the vector space $V_2$, namely
$$ F_{v} = \sum_{i=1}^n\lambda_i E_i \ \ \ \ \ (2) $$

My question is: does anyone know of a proof showing that the mapping $F_{v}$ defined by $(1)$, $(2)$ is independent of $v$? Is there a name for such an action? (for example, does such a mapping appear in some well-known theorem?) And for that matter: is there a name for such a mapping in general?


Of course, the only way the $F_v$s are really independent is

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