Writing down Mathematics with Arrays

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To write down array operations on paper, particularly for element-wise multiplication of matrices, the Hadamard or Schur product is used. When multiplying two matrices A and B element-wise to obtain a matrix C, the notation A · B = C can be misleading as it resembles the dot product. Clarity in notation is essential, and alternatives like A *_S B can be employed to specify the Schur product explicitly. The key is to ensure that the notation clearly communicates the operation being performed. Understanding the distinction between the ordinary product and the Schur product is crucial for accurate mathematical representation.
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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

A \cdot B = C

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 A *_S B.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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