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Certain function words such as and, the, at, a, etc., were placed in a "forbidden word list" table, and the frequency of these words was recorded in a separate listing... A special computer program, called the Descriptor Word Index Program, was written to provide this information and to prepare a document-term matrix in a form suitable for in ...
Power Query was first announced in 2011 under the codename "Data Explorer" as part of Azure SQL Labs. In 2013, in order to expand on the self-service business intelligence capabilities of Microsoft Excel, the project was redesigned to be packaged as an add-in Excel and was renamed "Data Explorer Preview for Excel" [4], and was made available for Excel 2010 and Excel 2013. [5]
word choice/wrong word: Incorrect or awkward word choice hr # Insert hair space: s/b: should be: Selection should be whatever edit follows this mark s/r: substitute/replace: Make the substitution tr: transpose: Transpose the two words selected vf: verb form (Mostly used when translating) The version of the verb is used incorrectly e: ending
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]
Multiplication of X by e i extracts the i-th column, while multiplication by B i puts it into the desired position in the final vector. Alternatively, the linear sum can be expressed using the Kronecker product : vec ( X ) = ∑ i = 1 n e i ⊗ X e i {\displaystyle \operatorname {vec} (\mathbf {X} )=\sum _{i=1}^{n}\mathbf {e} _{i}\otimes ...
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 .
Typically, the matrix is assumed to be stored in row-major or column-major order (i.e., contiguous rows or columns, respectively, arranged consecutively). Performing an in-place transpose (in-situ transpose) is most difficult when N ≠ M , i.e. for a non-square (rectangular) matrix, where it involves a complex permutation of the data elements ...
The last column can be fixed to any unit vector, and each choice gives a different copy of O(n) in O(n + 1); in this way O(n + 1) is a bundle over the unit sphere S n with fiber O(n). Similarly, SO( n ) is a subgroup of SO( n + 1) ; and any special orthogonal matrix can be generated by Givens plane rotations using an analogous procedure.