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  2. Row and column vectors - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_vectors

    The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: […] = [] and [] = […]. The set of all row vectors with n entries in a given field (such as the real numbers ) forms an n -dimensional vector space ; similarly, the set of all column vectors with m entries forms an m ...

  3. Vectorization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Vectorization_(mathematics)

    Multiplication of X by e i extracts the i-th column, while multiplication by B i puts it into the desired position in the final vector. Alternatively, the linear sum can be expressed using the Kronecker product : vec ⁡ ( X ) = ∑ i = 1 n e i ⊗ X e i {\displaystyle \operatorname {vec} (\mathbf {X} )=\sum _{i=1}^{n}\mathbf {e} _{i}\otimes ...

  4. NumPy - Wikipedia

    en.wikipedia.org/wiki/NumPy

    NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]

  5. Transpose - Wikipedia

    en.wikipedia.org/wiki/Transpose

    In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]

  6. Row- and column-major order - Wikipedia

    en.wikipedia.org/wiki/Row-_and_column-major_order

    As exchanging the indices of an array is the essence of array transposition, an array stored as row-major but read as column-major (or vice versa) will appear transposed. As actually performing this rearrangement in memory is typically an expensive operation, some systems provide options to specify individual matrices as being stored transposed.

  7. Permutation matrix - Wikipedia

    en.wikipedia.org/wiki/Permutation_matrix

    Multiplying a matrix M by either or on either the left or the right will permute either the rows or columns of M by either π or π −1.The details are a bit tricky. To begin with, when we permute the entries of a vector (, …,) by some permutation π, we move the entry of the input vector into the () slot of the output vector.

  8. Transpositions matrix - Wikipedia

    en.wikipedia.org/wiki/Transpositions_matrix

    The property of fours of matrices gives the possibility to create matrix with mutually orthogonal rows and columns (matrix ) by changing the sign to an odd number of elements in every one of fours (,,,,,), ,,, [,].

  9. Conjugate transpose - Wikipedia

    en.wikipedia.org/wiki/Conjugate_transpose

    The conjugate transpose "adjoint" matrix should not be confused with the adjugate, ⁡ (), which is also sometimes called adjoint. The conjugate transpose of a matrix A {\displaystyle \mathbf {A} } with real entries reduces to the transpose of A {\displaystyle \mathbf {A} } , as the conjugate of a real number is the number itself.