Search results
Results From The WOW.Com Content Network
In multilinear algebra, mode-m flattening [1] [2] [3], also known as matrixizing, matricizing, or unfolding, [4] is an operation that reshapes a multi-way array into a matrix denoted by [] (a two-way array). Matrixizing may be regarded as a generalization of the mathematical concept of vectorizing.
After flattening, arrays are represented as single-dimensional value vector V containing scalar elements, alongside auxiliary information recording the nested structure, typically in the form of a boolean flag vector F. The flag vector indicates, for the corresponding element in the value vector, whether it is the beginning of a new segment.
In other words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices. When A is an invertible matrix there is a matrix A −1 that represents a transformation that "undoes" A since its composition with A is the identity matrix. In some practical applications, inversion can be computed using ...
An increase of Laravel's userbase and popularity lined up with the release of Laravel 3. [1] Laravel 4, codenamed Illuminate, was released in May 2013. It was made as a complete rewrite of the Laravel framework, migrating its layout into a set of separate packages distributed through Composer, which serves as an application-level package manager.
There are three variants: the flattening , [1] sometimes called the first flattening, [2] as well as two other "flattenings" ′ and , each sometimes called the second flattening, [3] sometimes only given a symbol, [4] or sometimes called the second flattening and third flattening, respectively.
In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image. Or more simply, when each pixel in the output image is a function of the nearby pixels (including itself) in the input image ...
In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar.It is often denoted , .The operation is a component-wise inner product of two matrices as though they are vectors, and satisfies the axioms for an inner product.
Two downscaled images of the Flag of the Commonwealth of Nations. Before downscaling, a Gaussian blur was applied to the bottom image but not to the top image. The blur makes the image less sharp, but prevents the formation of moiré pattern aliasing artifacts. Gaussian blurring is commonly used when reducing the size of an image.