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Let be a vector space over a field equipped with a bilinear form. We define to be left-orthogonal to , and to be right-orthogonal to , when (,) = For a subset of , define the left-orthogonal complement to be = {: (,) = }.
To subtract a decimal number y (the subtrahend) from another number x (the minuend) two methods may be used: In the first method, the nines' complement of x is added to y . Then the nines' complement of the result obtained is formed to produce the desired result.
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
A conformal map acting on a rectangular grid. Note that the orthogonality of the curved grid is retained. While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum ...
If we condense the skew entries into a vector, (x,y,z), then we produce a 90° rotation around the x-axis for (1, 0, 0), around the y-axis for (0, 1, 0), and around the z-axis for (0, 0, 1). The 180° rotations are just out of reach; for, in the limit as x → ∞ , ( x , 0, 0) does approach a 180° rotation around the x axis, and similarly for ...
Many of us feel awkward accepting compliments—we might blush, avert eye contact, start mumbling in embarrassment, or even disparage ourselves. If that’s you, remember how good the person ...
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For years, whenever I wanted to compliment someone, I’d quote the film’s famous line: “That’ll do, Pig, that’ll do.” Recently, I finally got my husband to watch the movie with me.