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The determinant of a matrix A is denoted det(A), det A, or A. The Leibniz formula shows that the determinant of real (or analogously for complex) square matrices is a polynomial function from R n n {\displaystyle \mathbf {R} ^{n\times n}} to R {\displaystyle \mathbf {R} } . The same idea is also used in […]

At its simplest obviously this involves controlling the other conditions (for example temperature) so that all treatments experience identical conditions (though note that it may not always be necessary for the conditions to be constant—it may be sufficient that whatever variation occurs is the same for all treatments). The (statistical) design of experiments (DOE) is […]

What does this have to do with the (actual) mean value theorem, other than the semblance of the indeterminate ccc? Well, if F(x)F(x)F(x) is an antiderivative of f(xf(xf(x), the fundamental theorem of calculus (Newton-Leibniz formula) makes the left-hand side equal to F(b)−F(a)F(b) – F(a)F(b)−F(a), so that we haveF(b)−F(a)b−a=f(c)=F′(c). If f special info = 0 and […]