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Espai Dual

En aquesta pàgina encara no hi ha res escrit. Si vols començar, endavant!

Recursos

Since I haven't posted for a while, I decided to break up my rants about homology with some posts on linear (and multilinear) algebra. In this post, we will (as usual) deal only with finite dimensional vector spaces.

https://algebrology.github.io/dual-spaces/

Covector: The Long-Lost Twin of Vector?

First of all, let us review how the vector components change with different basis vectors. Consider the following diagram with unprimed basis vectors (blue) and primed basis vectors (green). Suppos…

Covector: The Long-Lost Twin of Vector?

https://almosttensorial.wordpress.com/covector-the-long-lost-twin-of-vector/

Covector: The Long-Lost Twin of Vector?

How do I find a dual basis given the following basis?

$V = \Bbb{R}^3$ and has basis $\mathcal{B} = \{\vec{e_1}-\vec{e_2},\vec{e_1}+\vec{e_2},\vec{e_3}\}$ How do I find the dual basis? This is not homework, but an example that I am struggling to grasp...

How do I find a dual basis given the following basis?

https://math.stackexchange.com/questions/1286100/how-do-i-find-a-dual-basis-given-the-following-basis

How do I find a dual basis given the following basis?

Understanding dual spaces

Time for a short preparatory post about vector spaces. This is a follow up of my differential form post…

Understanding dual spaces

https://medium.com/@luca.ambrogioni/understanding-dual-spaces-4b39d000a7ed

Understanding dual spaces

On the Visualization of the Dual Space

This post talks about visualization of the dual space $V^*$. To read it, you need to know what a vector space is. If you don’t, this post is not for you.

https://web.tecnico.ulisboa.pt/~ist189623/wordpress/2021/08/08/on-the-visualization-of-the-dual-space/

Espai Vectorial - Repàs

Previ

Estructures algebraiques així pim pam

Què és un espai vectorial?

Exemples típics d’espais vectorials

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Definició exacta d’un espai vectorial

📌

Un espai vectorial en general no té mètrica! (no hi ha producte escalar, ni norma i els vectors no estan ordenats ni tenen angles entre ells)

Relacionat

Dualitat (concepte matemàtic)

Dualitat (concepte matemàtic)