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- ...{u}</math> and <math>\mathbf{v}</math> as lying on the unit sphere in this subspace, which is isomorphic to <math>\mathbb{C}^2</math>. Another thing to note is13 KB (2,048 words) - 14:28, 22 February 2024
- Let <math>X</math> be a [[topological space]] and <math>S</math> be a [[subspace]] of <math>X</math>. Then <math>S</math> is '''dense''' in <math>X</math> i367 bytes (69 words) - 15:42, 18 August 2006
- .../math> and <math>B</math> be [[metric space]]s, let <math>A'</math> be a [[subspace]] of <math>A</math>, and, let <math>f</math> be a function from <math>A'</m7 KB (1,327 words) - 17:39, 28 September 2024
- ...ss the kernel of this matrix (also known as the null space), or the linear subspace of the domain of <math>\hat{T}</math> where everything gets mapped to the n15 KB (2,406 words) - 22:56, 23 November 2023
- ...ath> is a vector space itself (over the same field), then it is called a ''subspace'' of <math>V</math>. ...e set of all linear combinations of the elements of <math>X</math> forms a subspace of <math>V</math>. This space is said to have been generated by <math>X</m3 KB (561 words) - 23:47, 20 March 2009
- ...sposes of the rows form a subset of the vector space <math>F^n</math>. The subspace of <math>F^n</math> generated by these is known as the row space of <math>A The set <math>\{x:A_{m \times n}x_{n \times 1} = \phi\}</math> forms a subspace of <math>F^n</math>, known as the null space <math>N(A)</math> of <math>A</4 KB (856 words) - 14:29, 30 March 2013
- ...r <math>T \in \mathcal{T}</math>. This topology is called the topological subspace <math>S</math>. Note that open and closed sets in the subspace <math>S</math> are not necessarily open or closed in the space <math>X</mat6 KB (1,142 words) - 14:38, 21 June 2008
- ...nd with that eigenvalue, and is a [[vector space]]; in particular, it is a subspace of the domain of the map <math>L</math>.821 bytes (138 words) - 18:32, 2 March 2010
- ...For example, the set <math>(0,1) \cup (2,3)</math> is not connected as a [[subspace]] of <math>\mathbb{R}</math>. ...ine equivalence relation <math>x \sim y</math> if there exists a connected subspace of <math>X</math> containing <math>x,y</math>, then the resulting [[equival3 KB (497 words) - 15:27, 15 March 2010
- ...ce <math>\mathbb{R}_k</math>, the [[k-topology]] (or in more generality, a subspace of <math>\mathbb{R}</math> consisting of <math>\mathbb{R}</math> missing a5 KB (672 words) - 12:28, 4 June 2018
- ...ce of the Sorgenfrey plane, but it inherits the [[discrete topology]] as a subspace: consider the basis element given by <math>[x,x+1) \times [-x,-x+1)</math>. ...this because any subset <math>A</math> of <math>-\Delta</math> is a closed subspace of <math>\mathbb{R}_l^2</math>, and it can be shown that there do not exist1 KB (205 words) - 10:20, 26 May 2019
- ...in\text{R}(\text{T})</math>. Because <math>\text{R}(\text{T})</math> is a subspace (this is easy to verify), then the basis of <math>\text{R}(\text{T})</math>5 KB (893 words) - 21:41, 28 May 2022