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Este modulo definirá una norma y da unos ejemplos y sus propiedades.


Mucho del lenguaje utilizado en esta sección seráfamiliar para usted- debe de haber estado expuesto a los conceptos de

  • producto interno
  • ortogonalidad
  • expansión de base
en el contexto de n . Vamos a tomar lo que conocemos sobre vectores y aplicarlo a funciones (señales de tiempo continuo).


La norma de un vector es un número real que representa el "tamaño" de el vector.

En 2 , podemos definir la norma que sea la longitud geométrica de los vectores.

x x 0 x 1 , norma x x 0 2 x 1 2

Matemáticamente, una norma · es solo una función (tomando un vector y regresando un número real) que satisface tres reglas

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Para ser una norma, · debe satisfacer:

  • la norma de todo vector es positiva x x S x 0
  • escalando el vector, se escala la norma por la misma cantidad α x α x para todos los vectores x y escalares α
  • Propiedad del Triángulo: x y x y para todos los vectores x , y .“El“tamaño“de la suma de dos vectores es menor o igual a la suma de sus tamaños”

Un espacio vectorial con una norma bien definida es llamado un espacio vectorial normado o espacio lineal normado .


n n ), x x 0 x 1 x n - 1 , 1 x i 0 n 1 x i , n con esta norma es llamado 1 ( [ 0 , n - 1 ] ) .

Colección de todas las x 2 con 1 x 1
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n n ), con norma 2 x i 0 n 1 x i 2 1 2 , n es llamado 2 ( [ 0 , n - 1 ] ) (la usual "norma Euclideana").

Colección de todas las x 2 with 2 x 1
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n (or n , with norm x i x i is called ( [ 0 , n - 1 ] )

x 2 con x 1
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Espacios de secuencias y funciones

Podemos definir normas similares para espacios de secuencias y funciones.

Señales de tiempo discreto= secuencia de números x n x -2 x -1 x 0 x 1 x 2

  • 1 x n i x i , x n 1 ( ) 1 x
  • 2 x n i x i 2 1 2 , x n 2 ( ) 2 x
  • p x n i x i p 1 p , x n p ( ) p x
  • x n sup i | x [ i ] | , x n ( ) x

Para funciones continuas en el tiempo:

  • p f t t f t p 1 p , f t L p ( ) p f t
  • (En el intervalo) p f t t 0 T f t p 1 p , f t L p ( [ 0 , T ] ) p f t

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
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Source:  OpenStax, Señales y sistemas. OpenStax CNX. Sep 28, 2006 Download for free at http://cnx.org/content/col10373/1.2
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