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  2. Row and column spaces - Wikipedia

    en.wikipedia.org/wiki/Row_and_column_spaces

    It follows that the null space of A is the orthogonal complement to the row space. For example, if the row space is a plane through the origin in three dimensions, then the null space will be the perpendicular line through the origin. This provides a proof of the rank–nullity theorem (see dimension above).

  3. Kernel (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Kernel_(linear_algebra)

    The left null space of A is the same as the kernel of A T. The left null space of A is the orthogonal complement to the column space of A, and is dual to the cokernel of the associated linear transformation. The kernel, the row space, the column space, and the left null space of A are the four fundamental subspaces associated with the matrix A.

  4. Metric signature - Wikipedia

    en.wikipedia.org/wiki/Metric_signature

    The number v (resp. p) is the maximal dimension of a vector subspace on which the scalar product g is positive-definite (resp. negative-definite), and r is the dimension of the radical of the scalar product g or the null subspace of symmetric matrix g ab of the scalar product. Thus a nondegenerate scalar product has signature (v, p, 0), with v ...

  5. Singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Singular_value_decomposition

    Such an ⁠ ⁠ belongs to ⁠ ⁠ 's null space and is sometimes called a (right) null vector of ⁠. ⁠ The vector ⁠ x {\displaystyle \mathbf {x} } ⁠ can be characterized as a right-singular vector corresponding to a singular value of ⁠ A {\displaystyle \mathbf {A} } ⁠ that is zero.

  6. Diagonal matrix - Wikipedia

    en.wikipedia.org/wiki/Diagonal_matrix

    An identity matrix of any size, or any multiple of it is a diagonal matrix called a scalar matrix, for example, []. In geometry , a diagonal matrix may be used as a scaling matrix , since matrix multiplication with it results in changing scale (size) and possibly also shape ; only a scalar matrix results in uniform change in scale.

  7. Array (data structure) - Wikipedia

    en.wikipedia.org/wiki/Array_(data_structure)

    Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, [12] a three-dimensional array a block of data, etc.

  8. Zero matrix - Wikipedia

    en.wikipedia.org/wiki/Zero_matrix

    In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of m × n {\displaystyle m\times n} matrices, and is denoted by the symbol O {\displaystyle O} or 0 {\displaystyle 0} followed by subscripts corresponding to the ...

  9. Examples of vector spaces - Wikipedia

    en.wikipedia.org/wiki/Examples_of_vector_spaces

    The dimension of this vector space, if it exists, [a] is called the degree of the extension. For example, the complex numbers C form a two-dimensional vector space over the real numbers R . Likewise, the real numbers R form a vector space over the rational numbers Q which has (uncountably) infinite dimension, if a Hamel basis exists.