Writing down Mathematics with Arrays

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Discussion Overview

The discussion revolves around how to represent array operations, specifically the element-wise multiplication of matrices, on paper. Participants explore different notations and clarify the distinction between various types of matrix products.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses familiarity with basic matrix operations but seeks guidance on writing array operations, particularly element-wise multiplication.
  • Another participant suggests the Hadamard/Schur product as a relevant concept for element-wise multiplication.
  • A different participant emphasizes the ordinary product, indicating a potential misunderstanding of the original request.
  • There is a clarification that the Schur product is indeed intended for element-wise multiplication, contrasting it with the ordinary product.
  • A participant questions the notation for representing the Schur product, noting that using A · B = C resembles the notation for a dot product.
  • Another participant asserts that any notation can be used as long as it is clear that the Schur product is being referenced, mentioning an alternative notation A *_S B.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the preferred notation for the Schur product, and there are competing views regarding the appropriate terminology and representation of matrix operations.

Contextual Notes

The discussion highlights potential confusion between different types of matrix products and the importance of clear notation in distinguishing between them.

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I know how to do basic matrix operations, but sometimes I do calculations on computers and do array operations. How do I write down array operations on paper? For example, say I have two matrices, A and B, and I want to multiply them element by element.
 
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What you really want is the ordinary product at the top of the linked wiki article.
 
Integral said:
What you really want is the ordinary product at the top of the linked wiki article.

He seems to want to multiply them element-wise, which is was the Schur product is for.
 
So if I take the Schur product of A and B to get C, do I write

[tex]A \cdot B = C[/tex]

As far as notation goes, this looks exactly like a dot product.
 
You can use whatever notation for you that you want. What's important is that you know you're talking about the Schur product. I've seen some people use [tex]A *_S B[/tex].
 

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