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This matrix is a specific instance of a document-feature matrix where "features" may refer to other properties of a document besides terms. [1] It is also common to encounter the transpose, or term-document matrix where documents are the columns and terms are the rows.
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]
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 transpose of a matrix A, denoted by A T, [3] ⊤ A, A ⊤, , [4] [5] A′, [6] A tr, t A or A t, may be constructed by any one of the following methods: Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain A T; Write the rows of A as the columns of A T; Write the columns of A as the rows of A T
Power Pivot can scale to process very large datasets in memory, which allows users to analyze datasets that would otherwise surpass Excel's limit of one million rows. [9] Power Pivot allows for importing data from multiple sources, such as databases (SQL Server, Microsoft Access, etc.), OData data feeds, Excel files, and other sources ...
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 ...
The row space of this matrix is the vector space spanned by the row vectors. The column vectors of a matrix. The column space of this matrix is the vector space spanned by the column vectors. In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column ...
The conjugate transpose of a matrix with real entries reduces to the transpose of , as the conjugate of a real number is the number itself. The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2 × 2 {\displaystyle 2\times 2} real matrices, obeying matrix addition and multiplication: [ 3 ]
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