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Scan and read Data Matrix barcodes from image files is one of the barcode decoding functions in . NET Barcode Reader component. To help . net developers ... De nition Given random variables X1, X2, p , Xp and constants c1, c2, p , cp, Y c1 X1 c2 X2 p cp Xp (536) Figure C.3 The complex plane is generalized to three dimensions by introducing a second imaginary axis j. Just as multiplication by i rotates a vector along the real line out of its onedimensional world into the second dimension, multiplication by j rotates such a vector out of the real line into the third dimension. Just as multiplication by i twice means rotating 180 degrees (Le., inverting the direction of the vector), multiplication by j twice must also mean rotating 180 degrees. So just as i 2 = 1, j2 must also be 1. But by which number can we mUltiply a vector on the ordinary imaginary line to rotate it out of this Jine into the new imaginary line .net code 39 reader: Barcode Reader App for . NET  Code 39 C# & VB. NET Recognition ... .net data matrix reader Barcode Reader for . NET  How to Scan Data Matrix Using C# & VB ...
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The ASP. NET Data Matrix scanner control component can scan and decode Data Matrix barcode from image file in ASP. NET web site, VB. NET & C# class ... lines rather than just one. Now we can go not only from the real line to anyone of the other two imaginary lines, but we can also go from one of the imaginary lines to the other imaginary line. The former is solved by our straightforward extension of the old idea of mUltiplying by i: To get from the real line to the new imaginary line, we just multiply by the new imaginary number j. The latter, however, is still unresolved. There are two key questions that we must answer in order to complete our threedimensional generalization of the connection in two dimensions between multiplication of complex numbers and rotation: 1. By what number can we multiply a vector that lies on the iimaginary line to rotate it to the jimaginary line 2. Analogously, by what number can we multiply a vector that lies on the jimaginary line to rotate it to the iimaginary line Let us concentrate on question 1 first. Clearly, this number cannot be real, for it would only change the length or invert the direction of the vector without making it leave the iimaginary line. Neither can it be i nor j. It cannot be i, because ii = 1, which takes the vector to the real axis. It cannot be j because ji = j would imply that i = 1. So we are forced to assume the existence of a/ourth axis with a new unit number k, whose multiplication takes a vector on the iimaginary line onto the jimaginary line; that is, (C.7) ki = j. Being a fourth dimension, this new axis is at 90 degrees to the other axes. Then multiplication by k twice must mean a rotation of 180 degrees, which implies that x1 fX1 X2 p Xp 1x1, x2, p , xp 2 dx1 dx2 p dxp x2 fX1 X2 p Xp 1x1, x2, p , xp 2 dx1 dx2 p dxp xp fX1 X2 p Xp 1x1, x2, p , xp 2 dx1 dx2 p dxp cp Xp, c2E 1X2 2 p cp E 1Xp 2 (537) this forth axis is also an imaginary axis; that is, .net data matrix reader Reading 2D Barcode from Images  Stack Overflow
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