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  2. Row and column vectors - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_vectors

    In linear algebra, a column vector with ⁠ ⁠ elements is an matrix [1] consisting of a single column of ⁠ ⁠ entries, for example, = [].. Similarly, a row vector is a matrix for some ⁠ ⁠, consisting of a single row of ⁠ ⁠ entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)

  3. Matrix (mathematics) - Wikipedia

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

    Matrices can be used to compactly write and work with multiple linear equations, that is, systems of linear equations. For example, if A is an m×n matrix, x designates a column vector (that is, n×1-matrix) of n variables x 1, x 2, ..., x n, and b is an m×1-column vector, then the matrix equation =

  4. Row and column spaces - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_spaces

    The row space of this matrix is the vector space spanned by the row vectors. The column vectors of a matrix. The column space of this matrix is the vector space spanned by the column vectors. In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column ...

  5. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    For example, in attempting to find the maximum likelihood estimate of a multivariate normal distribution using matrix calculus, if the domain is a k×1 column vector, then the result using the numerator layout will be in the form of a 1×k row vector. Thus, either the results should be transposed at the end or the denominator layout (or mixed ...

  6. Transformation matrix - Wikipedia

    en.wikipedia.org/wiki/Transformation_matrix

    If A and B are the matrices of two linear transformations, then the effect of first applying A and then B to a column vector is given by: = (). In other words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices.

  7. Outer product - Wikipedia

    en.wikipedia.org/wiki/Outer_product

    The outer product is equivalent to a matrix multiplication, provided that is represented as a column vector and as a column vector (which makes a row vector). [ 2 ] [ 3 ] For instance, if m = 4 {\displaystyle m=4} and n = 3 , {\displaystyle n=3,} then [ 4 ]

  8. Vectorization (mathematics) - Wikipedia

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

    In Matlab/GNU Octave a matrix A can be vectorized by A(:). GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well. In Python NumPy arrays implement the flatten method, [note 1] while in R the desired effect can be achieved via the c() or as.vector() functions.

  9. Row- and column-major order - Wikipedia

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

    More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.