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A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
Differential 0-forms, 1-forms, and 2-forms are special cases of differential forms. For each k , there is a space of differential k -forms, which can be expressed in terms of the coordinates as ∑ i 1 , i 2 … i k = 1 n f i 1 i 2 … i k d x i 1 ∧ d x i 2 ∧ ⋯ ∧ d x i k {\displaystyle \sum _{i_{1},i_{2}\ldots i_{k}=1}^{n}f_{i_{1}i_{2 ...
deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform. dim – dimension of a vector space.
If only one root, say r 1, is real, then r 2 and r 3 are complex conjugates, which implies that r 2 – r 3 is a purely imaginary number, and thus that (r 2 – r 3) 2 is real and negative. On the other hand, r 1 – r 2 and r 1 – r 3 are complex conjugates, and their product is real and positive. [ 23 ]
In mathematics, the Chern–Simons forms are certain secondary characteristic classes. [1] The theory is named for Shiing-Shen Chern and James Harris Simons , co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.
3-point-form of a hyperbola's equation — The equation of the hyperbola determined by 3 points = (,), =,,, ,, is the solution of the equation () () = () () for . As an affine image of the unit hyperbola x 2 − y 2 = 1
Given a 3 × 3 rotation matrix R, a vector u parallel to the rotation axis must satisfy =, since the rotation of u around the rotation axis must result in u. The equation above may be solved for u which is unique up to a scalar factor unless R is the identity matrix I. Further, the equation may be rewritten