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Excel at using Excel with these keyboard hotkeys that will save you minutes of time—and hours of aggravation. The post 80 of the Most Useful Excel Shortcuts appeared first on Reader's Digest.
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 general inversion algorithms or by performing inverse operations (that have obvious geometric interpretation, like rotating ...
The vectorization is frequently used together with the Kronecker product to express matrix multiplication as a linear transformation on matrices. In particular, vec ( A B C ) = ( C T ⊗ A ) vec ( B ) {\displaystyle \operatorname {vec} (ABC)=(C^{\mathrm {T} }\otimes A)\operatorname {vec} (B)} for matrices A , B , and C of dimensions k ...
COMMAND. ACTION. Ctrl/⌘ + C. Select/highlight the text you want to copy, and then press this key combo. Ctrl/⌘ + F. Opens a search box to find a specific word, phrase, or figure on the page
For matrix-matrix exponentials, there is a distinction between the left exponential Y X and the right exponential X Y, because the multiplication operator for matrix-to-matrix is not commutative. Moreover, If X is normal and non-singular, then X Y and Y X have the same set of eigenvalues. If X is normal and non-singular, Y is normal, and XY ...
Excel for the web is a free lightweight version of Microsoft Excel available as part of Office on the web, which also includes web versions of Microsoft Word and Microsoft PowerPoint. Excel for the web can display most of the features available in the desktop versions of Excel, although it may not be able to insert or edit them.
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For example, if V is an m × n matrix, W is an m × p matrix, and H is a p × n matrix then p can be significantly less than both m and n. Here is an example based on a text-mining application: Let the input matrix (the matrix to be factored) be V with 10000 rows and 500 columns where words are in rows and documents are in columns. That is, we ...