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  2. Row and column spaces - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_spaces

    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 vectors. The column space of a matrix is the image or range of the corresponding ...

  3. Matrix (mathematics) - Wikipedia

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

    A matrix with the same number of rows and columns is called a square matrix. [5] A matrix with an infinite number of rows or columns (or both) is called an infinite matrix. In some contexts, such as computer algebra programs, it is useful to consider a matrix with no rows or no columns, called an empty matrix.

  4. 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.)

  5. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    A coordinate vector is commonly organized as a column matrix (also called a column vector), which is a matrix with only one column. So, a column vector represents both a coordinate vector, and a vector of the original vector space. A linear map A from a vector space of dimension n into a vector space of dimension m maps a column vector

  6. Row- and column-major order - Wikipedia

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

    While the terms allude to the rows and columns of a two-dimensional array, i.e. a matrix, the orders can be generalized to arrays of any dimension by noting that the terms row-major and column-major are equivalent to lexicographic and colexicographic orders, respectively. It is also worth noting that matrices, being commonly represented as ...

  7. List of named matrices - Wikipedia

    en.wikipedia.org/wiki/List_of_named_matrices

    Synonym for binary matrix or logical matrix. Alternant matrix: A matrix in which successive columns have a particular function applied to their entries. Alternating sign matrix: A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. Anti-diagonal ...

  8. Vectorization (mathematics) - Wikipedia

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

    Specifically, the vectorization of a m × n matrix A, denoted vec(A), is the mn × 1 column vector obtained by stacking the columns of the matrix A on top of one ...

  9. Square matrix - Wikipedia

    en.wikipedia.org/wiki/Square_matrix

    In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order . Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation.