# Maths notation: power raised after argument bracket

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.

• What do you mean when you say that "$Q(x)$ are the elements of a matrix"? Perhaps you could give some more context. – Ben W Aug 23 at 17:08
• 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. – Stinking Bishop Aug 23 at 17:15
• Right, @BenW . Are we looking at a matrix $Q(x)$ that’s different for each given $x$, or something else altogether? – Lubin Aug 23 at 17:16
• @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 $Q(1)$, $Q(2)$, $Q(3)$..... – RockTheBoat Aug 23 at 17:29
• @StinkingBishop You have a point! Thanks. The "wrong" convention in trigonometric functions is probably what led me to the confusion. – RockTheBoat Aug 23 at 17:32