vector: [ a b c d e f ] which I would like to convert into a 2D matrix. Let's arbitrarily say I'd like to ravel along the rows first (fill one row before moving to the next). [ a b c d e f ] Is there a series of multiplicative matrix transformations that performs this reshaping, and if so, what is the general name for this operation?

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vector:      [                            a                          b                          c                          d                          e                          f                      ]  which I would like to convert into a 2D matrix. Let&#039;s arbitrarily say I&#039;d like to ravel along the rows first (fill one row before moving to the next).      [                            a                          b                                      c                          d                                      e                          f                      ]  Is there a series of multiplicative matrix transformations that performs this reshaping, and if so, what is the general name for this operation?

SuefsSeeltHeRn8 · Accepted Answer

es, the operation is called matrixication (or the inverse operation of vectorization). From a formal perspective, the space of   m  ×  n matrices is isomorphic to the space of   m  n dimensional vectors. The isomorphism which establishes the the isomorphy is the vectorization operator       v    e    c  . This operator turns a matrix into a vector by stacking the columns. Since       v    e    c   is am isomorphism, there exists the inverse operation             v      e      c              −      1      , which turns a vector into a matrix by unstacking the vector.

Mohamed Mooney · Accepted Answer

It is not possible to do this by matrix multiplications: If   A  ,  B are matrices such that  A  v  B  =      (                            a                          b                                      c                          d                                      e                          f                      )  for all   v  =      (                            a                          b                          c                          d                          e                          f                      )  , then   A must be   3  ×  1 and   B must be   6  ×  2. But then   v  B is only   1  ×  2, which is too small for the six desired dimensions of the final result.

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