The dual space of a vector space $V$ over a field $k$ is the vector space of all linear maps from $V$ into $k$.
The dual space of a vector space $V$ over a field $k$ is the vector space of all linear maps from $V$ into $k$.
Questions tagged [dual-spaces]
1318 questions
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Multiplying Vectors and Covectors
$\begin{pmatrix}a\\b\\c\end{pmatrix}\begin{pmatrix}x&y&z\end{pmatrix}=\begin{pmatrix}ax&ay&az\\bx&by&bz\\cx&cy&cz\end{pmatrix}$ by regular matrix multiplication. But if
$\begin{pmatrix}a\\b\\c\end{pmatrix}$ is an element of the double dual space I…
Pineapple Fish
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Why is every $l^p(\mathbb{K})$ a dual of some normed space?
Why is every $l^p(\mathbb{K})$ a dual of some normed space?
The $l^p(\mathbb{K})$ space is the space:
$$\{ w \in F(\mathbb{N}, \mathbb{K}) : \sum_{n=0}^{\infty} |w(n)|^p < \infty\}$$
where $F(\mathbb{N}, \mathbb{K})$ is the space of functions $f:…
mavavilj
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Equivalence relation in dual spaces
Do the dual spaces satisfy equivalence relation?
For example the dual space of $\mathbb{R^n}$ is $\mathbb{R^n}$. Do the remaining two properties of equivalence relation can be applied to dual spaces, in general.
that is,
$Reflexivity, Symmetry,…
WKhan
- 107
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Annihilators and closedness
Let $E$ be a normed space. Let $A\subset E$ and $B \subset E^*$ be arbitrary subsets.
Then the annihilators $A^\perp$ and $B_\perp$ are closed subspaces of $E^*$ resp. $E$.
Why is that?
dba
- 999
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write function as sum of covectors
I've got what should be a simple question. I have a function f(x,y) = 3x + 2y
The question asks to write this function as a sum of dual vectors. Any help on where to begin?
