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  2. Bijection, injection and surjection - Wikipedia

    en.wikipedia.org/wiki/Bijection,_injection_and...

    The function is bijective (one-to-one and onto, one-to-one correspondence, or invertible) if each element of the codomain is mapped to by exactly one element of the domain; that is, if the function is both injective and surjective. A bijective function is also called a bijection.

  3. Vector projection - Wikipedia

    en.wikipedia.org/wiki/Vector_projection

    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 ...

  4. Injective function - Wikipedia

    en.wikipedia.org/wiki/Injective_function

    In mathematics, an injective function (also known as injection, or one-to-one function [1]) is a function f that maps distinct elements of its domain to distinct elements of its codomain; that is, x 1 ≠ x 2 implies f(x 1) ≠ f(x 2) (equivalently by contraposition, f(x 1) = f(x 2) implies x 1 = x 2).

  5. Bijection - Wikipedia

    en.wikipedia.org/wiki/Bijection

    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]

  6. Projection (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Projection_(linear_algebra)

    A square matrix is called a projection matrix if it is equal to its square, i.e. if =. [2]: p. 38 A square matrix is called an orthogonal projection matrix if = = for a real matrix, and respectively = = for a complex matrix, where denotes the transpose of and denotes the adjoint or Hermitian transpose of .

  7. Surjective function - Wikipedia

    en.wikipedia.org/wiki/Surjective_function

    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 ...

  8. Affine transformation - Wikipedia

    en.wikipedia.org/wiki/Affine_transformation

    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 ...

  9. Triangulation (computer vision) - Wikipedia

    en.wikipedia.org/wiki/Triangulation_(computer...

    In computer vision, triangulation refers to the process of determining a point in 3D space given its projections onto two, or more, images. In order to solve this problem it is necessary to know the parameters of the camera projection function from 3D to 2D for the cameras involved, in the simplest case represented by the camera matrices.