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An finite ordered set of n elements is called a n-tuple, and is commonly denoted with parenthesis, e.g. (1, 2,..., 5) for the 5-tuple of 1 to 5. But this notation clashes with open intervals, when working with 2-tuples. So you should probably add some explanatory text depending on who your target audience is.
From this definition, the null space of A is the set of all vectors such that Av = 0. Obviously v = [0, 0, 0,..., 0] is part of the null space, so it is always non-empty. The rank of the matrix is related to the range. It denotes how many columns of A are actually "relevant" in determining its range. You may think that removing a column from a ...
However, polynomials, primarily even-degree ones, do NOT use all the Real numbers as outputs. The outputs a particular function actually uses from the set of all Reals is the image, also sometimes called the range. Thus, what could come out of a function is the codomain, but what actually comes out is the image (or range).
3. At least in Belgium, high schoolers get taught that n ∈ [a, b] n ∈ [a, b] is the standard notation for a given range of real numbers, so I wouldn't use it straight away. As others have pointed out though, introducing it beforehand is probably the best way to go from a practical standpoint. In my personal opinion, "Let x ∈ N ∩ [a, b ...
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Look at the top of the range: if it is odd then add 1, if even leave alone. Look at the bottom of the range: if it is odd then subtract 1, if even leave alone. Take the difference between the new even top and bottom; then divide by two. So for the range $[1,100]$ you get $\frac{100-0}{2}=50$ odd integers.
I was wondering how can I shift my data that fall between a range lets say [0, 125] to another range like [-128, 128]. Thanks for any help elementary-number-theory
1. modified 1 hour ago. 1 vote. 1 answer. 19 views. To prove if there exists a linear transformation that takes a high dimensional complex vector to a scalar injectively. complex-analysis. Matsmir. 3,570.
The range (properly called the image) of a function is the set into which the function actually maps. An example that would be similar to your problem is f: R → R f: R → R by f(x) = x2 f (x) = x 2. Although the codomain of f(x) = x2 f (x) = x 2 is R R, f(x) =x2 f (x) = x 2 truly only maps into the non-negative real numbers.
The key is that the kernel of a matrix is the orthogonal complement to the range of its transpose.