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

IntroducciÓN

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).

Normas

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 .

Ejemplos

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

a perfect square v²+2v+_
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or infinite solutions?
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Kristine 2*2*2=8
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Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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J, combine like terms 7x-4y
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f(n)= 2n + 1
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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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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