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Why is this matrix multiplication not associative?

Apologies for the low quality of the attached image.

Presented is an attempt to calculate the product of six matrices of size 3x3. The product: {{1,0,0},{0,1,0},{0,0,9}}

I then split the multiplication into two halves: The product of the first half: {{1,0,0},{-1,1,0},{2,-4,1}} The product of the second half: {{1,4,0},{0,1,3},{0,0,9}}

Multiplying these two matrices yields {{1,4,0},{-1,-3,3},{2,4,-3}}, which is correct. This is in fact the matrix which I row reduced to obtain the six elementary matrices in the original product.

Is there a reason why Wolfram|Alpha is computing the first result?

Six matrices

First three

Second three

First three, second three combined

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POSTED BY: E Nakamoto
3 Replies
Posted 5 years ago

Putting either a . or the word dot between each pair of matricies appears to make WolframAlpha perform matrix multiplication as you expect.

6 matricies with .

6 matricies with dot

POSTED BY: Bill Nelson

Taking a wild guess, the first one might be doing element-wise products rather than matrix multiplication.

POSTED BY: Daniel Lichtblau

That does make sense, thank you!

How might I "force" Wolfram to multiply normally? Moreover, why are the two smaller computations done normally?

POSTED BY: E Nakamoto
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