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A cross product on a Euclidean space V is a bilinear map from V × V to V, mapping vectors x and y in V to another vector x × y also in V, where x × y has the properties [1] [6] orthogonality : x ⋅ ( x × y ) = ( x × y ) ⋅ y = 0 , {\displaystyle \mathbf {x} \cdot (\mathbf {x} \times \mathbf {y} )=(\mathbf {x} \times \mathbf {y} )\cdot ...
In mathematics, a cube root of a number x is a number y such that y 3 = x.All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots.
Degree 7 – septic (or, less commonly, heptic) Degree 8 – octic; Degree 9 – nonic; Degree 10 – decic; Names for degree above three are based on Latin ordinal numbers, and end in -ic. This should be distinguished from the names used for the number of variables, the arity, which are based on Latin distributive numbers, and end in -ary.
The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
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