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Programming languages that implement matrices may have easy means for vectorization. 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 multilinear algebra, a reshaping of tensors is any bijection between the set of indices of an order-tensor and the set of indices of an order-tensor, where <.The use of indices presupposes tensors in coordinate representation with respect to a basis.
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
Note how the use of A[i][j] with multi-step indexing as in C, as opposed to a neutral notation like A(i,j) as in Fortran, almost inevitably implies row-major order for syntactic reasons, so to speak, because it can be rewritten as (A[i])[j], and the A[i] row part can even be assigned to an intermediate variable that is then indexed in a separate expression.
Some compiled languages such as Ada and Fortran, and some scripting languages such as IDL, MATLAB, and S-Lang, have native support for vectorized operations on arrays. For example, to perform an element by element sum of two arrays, a and b to produce a third c , it is only necessary to write
^ The current default format is binary. ^ The "classic" format is plain text, and an XML format is also supported. ^ Theoretically possible due to abstraction, but no implementation is included. ^ The primary format is binary, but text and JSON formats are available. [8] [9]
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices.Elements of the main diagonal can either be zero or nonzero.
The YIQ representation is sometimes employed in color image processing transformations. For example, applying a histogram equalization directly to the channels in an RGB image would alter the color balance of the image.