Bounded operator and Projection (linear algebra)

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Bounded operator and Projection (linear algebra)

Bounded operator vs. Projection (linear algebra)

In functional analysis, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded above by the same number, over all non-zero vectors v in X. In other words, there exists some M\ge 0 such that for all v in X The smallest such M is called the operator norm \|L\|_ \, of L. A bounded linear operator is generally not a bounded function; the latter would require that the norm of L(v) be bounded for all v, which is not possible unless L(v). In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

Similarities between Bounded operator and Projection (linear algebra)

Bounded operator and Projection (linear algebra) have 6 things in common (in Unionpedia): Banach space, Functional analysis, Linear map, Matrix (mathematics), Normed vector space, Operator algebra.

Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.

Banach space and Bounded operator · Banach space and Projection (linear algebra) · See more »

Functional analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.

Bounded operator and Functional analysis · Functional analysis and Projection (linear algebra) · See more »

Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

Bounded operator and Linear map · Linear map and Projection (linear algebra) · See more »

Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Bounded operator and Matrix (mathematics) · Matrix (mathematics) and Projection (linear algebra) · See more »

Normed vector space

In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined.

Bounded operator and Normed vector space · Normed vector space and Projection (linear algebra) · See more »

Operator algebra

In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings.

Bounded operator and Operator algebra · Operator algebra and Projection (linear algebra) · See more »

The list above answers the following questions

What Bounded operator and Projection (linear algebra) have in common
What are the similarities between Bounded operator and Projection (linear algebra)

Bounded operator and Projection (linear algebra) Comparison

Bounded operator has 38 relations, while Projection (linear algebra) has 66. As they have in common 6, the Jaccard index is 5.77% = 6 / (38 + 66).

References

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