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In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa.
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal.
The research-based design process is a research process proposed by Teemu Leinonen, [1] [2] inspired by several design theories. [ 3 ] [ 4 ] [ 5 ] It is strongly oriented towards the building of prototypes and it emphasizes creative solutions, exploration of various ideas and design concepts, continuous testing and redesign of the design solutions.
With post-process deduplication, new data is first stored on the storage device and then a process at a later time will analyze the data looking for duplication. The benefit is that there is no need to wait for the hash calculations and lookup to be completed before storing the data, thereby ensuring that store performance is not degraded ...
Duplication, or doubling, multiplication by 2; Duplication matrix, a linear transformation dealing with half-vectorization; Doubling the cube, a problem in geometry also known as duplication of the cube; A type of multiplication theorem called the Legendre duplication formula or simply "duplication formula"
"Don't repeat yourself" (DRY), also known as "duplication is evil", is a principle of software development aimed at reducing repetition of information which is likely to change, replacing it with abstractions that are less likely to change, or using data normalization which avoids redundancy in the first place.
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
One other popular approach is the Recursive Feature Elimination algorithm, [15] commonly used with Support Vector Machines to repeatedly construct a model and remove features with low weights. Embedded methods are a catch-all group of techniques which perform feature selection as part of the model construction process.