Apologies if this is a very basic question, but I came across a somewhat confusing notation and am not familiar with it. I am reading an article that contains the following notation in some of its equations:

$\sum_n a_n Q(x)^n $

where $Q(x)$ are the elements of a matrix.

My question: What does $Q(x)^n$ here mean? If we know the numerical value of $Q(x)$, then does $Q(x)^n$ simply mean "the value of $Q(x)$ raised to the power $n$"? [If it were indeed the $n$-th power, I personally would have expected it to be written as $Q^n(x)$.] Or could there be some other meaning to this?

I do note, there are similar questions answered on StackExchange, such as Conventions for function notation and Notation of a function raised to a power , but they do not refer to matrix elements; hence this post.

  • $\begingroup$ What do you mean when you say that "$Q(x)$ are the elements of a matrix"? Perhaps you could give some more context. $\endgroup$ – Ben W Aug 23 at 17:08
  • $\begingroup$ If it was raised to the $n$-th power, I would expect it to be written exactly as $Q(x)^n$. If you write $Q^n(x)$, this in most contexts means that $n$-th power of $Q$ was taken first, and only then you applied that to $x$. (Which, again, in most contexts, means $Q(Q(\ldots Q(x)\ldots))$.) Sadly, for trigonometric functions, this convention is not followed, so $\sin^2x$ means $(\sin x)^2$ rather than $\sin(\sin x)$ - however this is really an exception rather than a rule. $\endgroup$ – Stinking Bishop Aug 23 at 17:15
  • $\begingroup$ Right, @BenW . Are we looking at a matrix $Q(x)$ that’s different for each given $x$, or something else altogether? $\endgroup$ – Lubin Aug 23 at 17:16
  • $\begingroup$ @BenW Very good question. The article that mentions this notation is written in a highly abstract fashion and sadly does not clarify this. But from what I understand, $Q(x)$ refers to a series of values $Q(1)$, $Q(2)$, $Q(3)$..... $\endgroup$ – RockTheBoat Aug 23 at 17:29
  • $\begingroup$ @StinkingBishop You have a point! Thanks. The "wrong" convention in trigonometric functions is probably what led me to the confusion. $\endgroup$ – RockTheBoat Aug 23 at 17:32

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