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2. Linear algebra - Wikipedia

   en.wikipedia.org/wiki/Linear_algebra

   Functional analysis applies the methods of linear algebra alongside those of mathematical analysis to study various function spaces; the central objects of study in functional analysis are L p spaces, which are Banach spaces, and especially the L 2 space of square-integrable functions, which is the only Hilbert space among them. Functional ...

3. Outline of linear algebra - Wikipedia

   en.wikipedia.org/wiki/Outline_of_linear_algebra

   Examples of vector spaces; Linear map. Shear mapping or Galilean transformation; Squeeze mapping or Lorentz transformation; Linear subspace. Row and column spaces; Column space; Row space; Cyclic subspace; Null space, nullity; Rank–nullity theorem; Nullity theorem; Dual space. Linear function; Linear functional; Category of vector spaces

4. Operator (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Operator_(mathematics)

   This is why very different techniques are employed when studying linear operators (and operators in general) in the infinite-dimensional case. The study of linear operators in the infinite-dimensional case is known as functional analysis (so called because various classes of functions form interesting examples of infinite-dimensional vector ...

5. Linear function - Wikipedia

   en.wikipedia.org/wiki/Linear_function

   Here a denotes a constant belonging to some field K of scalars (for example, the real numbers) and x and y are elements of a vector space, which might be K itself. In other terms the linear function preserves vector addition and scalar multiplication. Some authors use "linear function" only for linear maps that take values in the scalar field ...

6. Linearity - Wikipedia

   en.wikipedia.org/wiki/Linearity

   In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.

7. Basis (linear algebra) - Wikipedia

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

   The same vector can be represented in two different bases (purple and red arrows). In mathematics, a set B of vectors in a vector space V is called a basis (pl.: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B.