Recent content by alQpr

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    Cross Product - Determinant form

    By "space" I just meant a vector space. The set of 3D vectors is one example but we can also consider higher dimensional spaces like R^n (or even infinite dimensional ones as well), and the "dual space" is a set of linear functions of vectors in the space - that is number-valued functions with...
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    Cross Product - Determinant form

    One definition of the determinant is as the unique (up to a constant) totally antisymmetric multilinear function on n vectors in n dimensions. Thinking of n-1 of the arguments (rows or columns) held fixed makes this a linear function on the remaining argument which is thus an element of the dual...
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    Infinitesimal Distances - A Question

    Defining df(a,\Delta x)=f'(a)\Delta x, and identifying x with the identity function x(x)=x, leaves us with dx(a,\Delta x)=\Delta x; but (I thought I was agreeing with you that) it would be a bad idea to suggest that this justifies taking dx as the same as \Delta x. PS I have edited my original...
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    Infinitesimal Distances - A Question

    Previous responders (and the Analysis book you referred to) have helped clarify the use of dx to denote a differential, and although I tend to agree with Studiot who says it is a "bad idea" (to identify dx with \Delta x) it is in fact standard notation used as you describe when you say we should...
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