I need to transform a 15x1 matrix into a 3x5 one. Is the first 3x1 column at the top, as Wikipedia seems to suggest?
2026-03-25 14:22:29.1774448549
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How to "de-vectorise" a matrix? Is first column at the bottom or at the top?
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There is not just one correct way to do it. The important part is to do it the same way as how you vectorized it. So just remember how you did that and you shall be fine.
The most common ones are probably column by column or row by row. But also different kinds of zig-zag patterns are used, for example in media codecs of various kinds.
Example of zig-zag pattern (credits to Aleks Khristov, wikipedia entry for JPEG, public domain):
There is no universally "correct" way to devectorize a matrix.
However, the column-major devectorization described by Wikipedia is the most common one in several contexts including linear algebra (cf. Horn and Johnson's Topics in Matrix Analysis) and multilinear algebra. Note that some authors prefer the row-major convention (cf. Watrous' Theory of Quantum Information).