Search results
Results from the WOW.Com Content Network
A function is bijective if it is both injective and surjective. A bijective function is also called a bijection or a one-to-one correspondence (not to be confused with one-to-one function, which refers to injection). A function is bijective if and only if every possible image is mapped to by exactly one argument. [1]
The function f : R → R defined by f(x) = x 3 − 3x is surjective, because the pre-image of any real number y is the solution set of the cubic polynomial equation x 3 − 3x − y = 0, and every cubic polynomial with real coefficients has at least one real root. However, this function is not injective (and hence not bijective), since, for ...
Functions which satisfy property (4) are said to be "one-to-one functions" and are called injections (or injective functions). [2] With this terminology, a bijection is a function which is both a surjection and an injection, or using other words, a bijection is a function which is both "one-to-one" and "onto". [3]
Let , the function to be estimated, be a real or complex valued function, and let the comparison function, be a real valued function. Let both functions be defined on some unbounded subset of the positive real numbers, and () be non-zero (often, but not necessarily, strictly positive) for all large enough values of . [4] One writes = (()) and it is read " is big O of ()" or more often "() is ...
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
From January 2008 to December 2012, if you bought shares in companies when Jim C. Walton joined the board, and sold them when he left, you would have a 43.9 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
The projection of a onto b is often written as or a ∥b. The vector component or vector resolute of a perpendicular to b , sometimes also called the vector rejection of a from b (denoted oproj b a {\displaystyle \operatorname {oproj} _{\mathbf {b} }\mathbf {a} } or a ⊥ b ), [ 1 ] is the orthogonal projection of a onto the plane (or ...
From January 2008 to December 2012, if you bought shares in companies when Frank A. Olson joined the board, and sold them when he left, you would have a -47.1 percent return on your investment, compared to a -2.8 percent return from the S&P 500.