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> However, the multiplication of a cracovian by another cracovian is defined differently: the result of multiplying an element from column i of the left cracovi
by kubb 1y ago
> However, the multiplication of a cracovian by another cracovian is defined differently: the result of multiplying an element from column i of the left cracovian by an element from column j of the right cracovian is a term of the sum in column i and row j of the result.
Am I the only one for whom this crucial explanation didn’t click? Admittedly, I might be stupid.
Wikipedia is a bit more understandable: „The Cracovian product of two matrices, say A and B, is defined by A ∧ B = (B^T)A
- tempodox 1y agoYou're not the only one. That “explanation” is just really bad.
- tgv 1y agoIt's the crucial part, and even with the example, I couldn't understand it. Like I can't understand why the second column in the first matrix doesn't have signs. Or why the 0 in the result matrix is negative. But in another link I found that it's column by column multiplication. So A × B = C, then C[i][j] = sum(A[k][i] * B[k][j]). Unfortunately, the example doesn't match that definition...
- burnished 1y agoNo, I think it is too ambiguous to be useful. The example wasn't helpful either, I think they needed to perform the individual calculations for clarity.
- kubb 1y agoYeah, usually you name the matrix elements a, b, c, d, etc. and write out the formula for the elements of the result.
- AdamH12113 1y agoThe example is simply wrong, according to other sources. This along with the inconsistent formatting makes me wonder if it was written by an LLM. It's a shame; this seems like an interesting topic.
- andrewla 1y agoAgreed -- "is a term of the sum" is such an inverted way to look at it. Better I think would be to say "the result in column i and row j is the sum of product of elements in column i of the left cracovian and column j of the right cracovian". And even by this definition the example given doesn't seem to track (and the strangeness of sometimes saying "+" and sometimes not, and having both "0" and "-0" in the example is bananas!): { 3 2 } { 1 -4 } = { 5 -2 } { -1 0 } { -2 3 } = { 0 2 } 3 * 1 + -1 * -2 == 5 -- check 3 * -4 + -1 * 3 == -15 -- what? 2 * 1 + 0 * -2 == 2 (okay, but shouldn't this be in the lower left, column 1 dotted with column 2?) 2 * -4 + 0 * 3 = -8 (now I'm really missing something)
- mci 1y agoThanks for the feedback, everyone. I pasted my Polish text into Gemini to translate it into English. Gemini hallucinated the translation of this example. Now it should be OK.
- mci 1y agoI took the liberty to replace my awkward wording with your "the result in column i and row j is the sum of product of elements in column i of the left cracovian and column j of the right cracovian". Hope you don't mind. Thanks!