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The main difference between forms 1042 and 1042-S is that form 1042-S is concerned with payments made to foreign persons, while form 1042 is concerned with determining how much income will be withheld for tax withholding purposes. Also, Form 1042-S must always be filed together with Form 1042-T, [3] but Form 1042 can be filed by itself.
Consider the vectors (polynomials) p 1 := 1, p 2 := x + 1, and p 3 := x 2 + x + 1. Is the polynomial x 2 − 1 a linear combination of p 1, p 2, and p 3? To find out, consider an arbitrary linear combination of these vectors and try to see when it equals the desired vector x 2 − 1. Picking arbitrary coefficients a 1, a 2, and a 3, we want
This work is in the public domain in the United States because it is a work prepared by an officer or employee of the United States Government as part of that person’s official duties under the terms of Title 17, Chapter 1, Section 105 of the US Code.
Top: The action of M, indicated by its effect on the unit disc D and the two canonical unit vectors e 1 and e 2. Left: The action of V ⁎, a rotation, on D, e 1, and e 2. Bottom: The action of Σ, a scaling by the singular values σ 1 horizontally and σ 2 vertically. Right: The action of U, another rotation.
The squared Euclidean distance between two points, equal to the sum of squares of the differences between their coordinates; Heron's formula for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares) The British flag theorem for rectangles equates two sums of two squares
The SVD decomposes M into three simple transformations: a rotation V *, a scaling Σ along the rotated coordinate axes and a second rotation U. Σ is a (square, in this example) diagonal matrix containing in its diagonal the singular values of M, which represent the lengths σ 1 and σ 2 of the semi-axes of the ellipse.
Code page 1042 (CCSID 1042), also known as Simplified Chinese PC Data Extended, is a single byte character set (SBCS) used by IBM in its PC DOS operating system in China. [1] [2] This code page is intended for use with code page 928 (Simplified Chinese double byte character set). [1] [3] [4] It is an extension of Code page 903.
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables.. Traditional notation uses a halo system, where symbols are placed as superscript or subscript before or after the main letter.