# Tag Archives: multilinear algebra

## Einstein-Penrose ‘s strong sum convention

the rank one tensors’ basis changes Filed under math, mathematics, multilinear algebra, word algebra

## wedge product example

When bivectors are defined by $\beta^i\wedge\beta^j:=\beta^i\otimes\beta^j-\beta^j\otimes\beta^i$,

so, for two generic covectors $\theta=a\beta^1+b\beta^2+c\beta^3$ and $\phi=d\beta^1+e\beta^2+f\beta^3$,

we have the bivector $\theta\wedge\phi=(bf-ce)\beta^2\wedge\beta^3+(cd-af)\beta^3\wedge\beta^1+(ad-be)\beta^1\wedge\beta^2$.

Otherwise,

Cf. this with the data $\left(\begin{array}{c}a\\b\\c\end{array}\right)$ and $\left(\begin{array}{c}d\\e\\f\end{array}\right)$ to construct the famous $\left(\begin{array}{c}a\\b\\c\end{array}\right)\times\left(\begin{array}{c}d\\e\\f\end{array}\right)=\left(\begin{array}{c}bf-ce\\cd-af\\ad-be\end{array}\right)$

So, nobody should be confused about the uses of the symbol $\wedge$ dans le calcul vectoriel XD

## need more?

¿necesitas o requieres un tema en particular? si es alrededor de álgebra multilineal, anímate a interaccionar. También tenemos topología de dimensiones bajas y más…

Filed under math

## real elementary multilinear algebra

are the common algebraic-techniques  territory for today vector algebra and differential geometry.

This means that ancient vectorcalculus that turns into differential forms nowadays, is “super-oversimplified” into a mathematical language to phrase some modern geometricalalgebrotopologicalanalitic-maths.

Real, ‘cuz first you gotta get the ideas over the field $\mathbb{R}$.

## local math brochures

Follow the links to get acquainted with the contents what we will work this semester.

They are

Also, let me feedback you mentioning the topics which can be get into it to work on thesis (B.Sc. or M.Sc.) or else

• differential geometry
• differential topology
• low dimensional topology
• algebra  and analysis
• sum of reciprocal inverses integers problem

These are fun  really!