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FarPoint Spread for Windows Forms is a Microsoft Excel-compatible spreadsheet component for Windows Forms applications developed using Microsoft Visual Studio and the .NET Framework. Developers use it to add grids and spreadsheets to their applications, and to bind them to data sources. [ 5 ]
transpose: Transpose the two words selected vf: verb form (Mostly used when translating) The version of the verb is used incorrectly e: ending: The ending of the word is incorrect / needs to be changed c: capitalization: Certain word needs to be capitalized
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]
The earliest editors (designed for teleprinter terminals) provided keyboard commands to delineate a contiguous region of text, then delete or move it. Since moving a region of text requires first removing it from its initial location and then inserting it into its new location, various schemes had to be invented to allow for this multi-step process to be specified by the user.
When one trades the inner product for the dual pairing, one can define the adjoint, also called the transpose, of an operator :, where , are Banach spaces with corresponding norms ‖ ‖, ‖ ‖. Here (again not considering any technicalities), its adjoint operator is defined as A ∗ : F ∗ → E ∗ {\displaystyle A^{*}:F^{*}\to E^{*}} with
where denotes the transpose of and is a fixed nonsingular, skew-symmetric matrix.This definition can be extended to matrices with entries in other fields, such as the complex numbers, finite fields, p-adic numbers, and function fields.
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
Visual understanding of multiplication by the transpose of a matrix. If A is an orthogonal matrix and B is its transpose, the ij-th element of the product AA T will vanish if i≠j, because the i-th row of A is orthogonal to the j-th row of A. An orthogonal matrix is the real specialization of a unitary matrix, and thus always a normal matrix.