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I know that the BEDMAS rules (Brackets - Exponents - Division OR Multiplications - Addition OR Subtraction) for Order of Operations apply to scalars and algebraic expressions.

Do the BEDMAS rules for Order of Operations apply to other "Mathematical Objects", such as Matrices or Vectors? (I am in high school, so I am not sure if there are any other types of "mathematical objects")

For instance, do the BEDMAS rules apply for the following expression with matrices:

$5A+3B$

Where in this case the scalar multiplication would be evaluated first, followed by Addition So that $5A+3B = (5A) + (3B)$ ,

What about a case involving matrix multiplication:

$A × B + C × D$

Would Matrix Multiplication be computed first, followed by Addition?

Such that: $ A × B + C × D = (A × B) + (C × D) $

Or in the case involving cross product of vectors? Would the cross product operation be interpreted as a multiplication operation and take precedence over addition?

Eg. $ u × v + w = (u × v) + w $ instead of: $ u × v + w = u × (v + w)$

I know this seems like a very straightforward question, and it would make sense that the BEDMAS rules would also apply to other mathematical objects. However, since this is not explicitly taught I want to make sure.

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  • $\begingroup$ Typically yes. If the answer is ever no for a specific context then it would be explicitly said so. $\endgroup$
    – JMoravitz
    Dec 24, 2023 at 3:07
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    $\begingroup$ "I am unsure if there are other types of mathematical objects" There are as many as the world's collective imagination allows and then some. Yes there are more, but learn them as you get to them. Remember that the problems we want to solve come first, and the definitions and new objects come after and are designed in such a way to be useful for those problems. $\endgroup$
    – JMoravitz
    Dec 24, 2023 at 3:10
  • $\begingroup$ So would Matrix Multiplication have the same priority as Scalar Multiplication (ie. before matrix addition/subtraction) ? $\endgroup$
    – Nefeli
    Dec 26, 2023 at 23:40
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    $\begingroup$ Yes, noting that $(kA)B = k(AB)$ they are on the same priority level with no ambiguity. You can also see scalar multiplication as multiplication by a scaled identity matrix $kA = (kI)A$ $\endgroup$
    – JMoravitz
    Dec 27, 2023 at 6:07
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    $\begingroup$ If you are ever unsure how it would be interpreted without parentheses... just use parentheses. That said, my initial comment still applies. "Typically yes" $\endgroup$
    – JMoravitz
    Dec 29, 2023 at 3:24

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Yes, they do. However, there is some additional complexity introduced by different sorts of mathematical objects not traditionally covered by the BEDMAS acronym.

For example, when functions are written without parenthesis, there are certain conventions that are assumed. $\sin 3 + x$ means $\sin (3) + x$ and not $\sin(3 + x)$, whereas $\sin 3x$ means $\sin(3x)$ and not $\sin(3) \cdot x$. However, $\sin 3 \sin x$ means $(\sin 3)(\sin x)$ and not $\sin(3 \sin (x))$. The conventions here are admittedly a little bit strange, but the more you become familiar with mathematical conventions, the easier it becomes to read mathematical expressions in the standard way.

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    $\begingroup$ I'm not sure about the first one. Personally, if I see $\sin 3 + x$ I would hesitate a lot. I feel like how I will interpret it in the end largely depends on how it is written, like whether $3 + x$ are written closely together or whether $\sin 3$ are written together and $+ x$ are somewhat farther apart. $\endgroup$
    – David Gao
    Dec 24, 2023 at 5:25
  • $\begingroup$ Thank you! So do the BEDMAS rules of priority basically apply to all mathematical expressions involving any types of "mathematical objects"? $\endgroup$
    – Nefeli
    Dec 25, 2023 at 1:00
  • $\begingroup$ @Nefeli When you are using them in contexts where BEDMAS applies, yes. The example I provided functions written without parenthesis is not covered by BEDMAS so its own set of special rules apply. $\endgroup$ Dec 25, 2023 at 5:07

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