cofactor

In linear algebra, the cofactor (sometimes called adjunct, see below) describes a particular construction that is useful for calculating both the determinant and inverse of square matrices. Specifically the cofactor of the (i, j) entry of …

In linear algebra, the cofactor (sometimes called adjunct, see below) describes a particular construction that is useful for calculating both the determinant and inverse of square matrices. Specifically the cofactor of the (i, j) entry of a matrix, also known as the (i, j) cofactor of that matrix, is the signed minor of that entry.

Finding the minors of a matrix A is a multi-step process:

Fields

In abstract algebra, a field is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms. The most commonly used fields are the field of real numbers, the field of complex numbers…

In abstract algebra, a field is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms. The most commonly used fields are the field of real numbers, the field of complex numbers, and the field of rational numbers, but there are also finite fields, fields of functions, various algebraic number fields, p-adic fields, and so forth.Any

magmas

In abstract algebra, an algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic struc…

In abstract algebra, an algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The notion of algebraic structure has been formalized in universal algebra.
Types of magmasMagmas are not often studied as such;

Griffiths 1.9

A particle of mass is in the state , where and are positive real constants.

Find A
Find the potential energy function
Calculate the expected values of
Find and . Is their product consistent with the uncertainty principle?

A particle of mass m is in the state \Psi(x,t)=A e^{-a\left( \frac{mx^2}{\hbar}+i t\right)}, where A and a are positive real constants.

  1. Find A
  2. Find the potential energy function V(x)
  3. Calculate the expected values of x, x^2, p, p^2
  4. Find \sigma_x and \sigma_p. Is their product consistent with the uncertainty principle?

\displaystyle \int_{-\infty}^\infty A^2 e^{-2a\left( \frac{mx^2}{\hbar}\right)}\,dx=2A^2\sqrt{\frac{\hbar}{2am}}\int_{0}^\infty \sqrt{\frac{2am}{\hbar}} e^{-2a\left( \frac{mx^2}{\hbar}\right)}\,dx=2A^2\sqrt{\frac{\hbar\pi}{2am}}=1

\displaystyle \displaystyle A^2=\sqrt{\frac{am}{2\pi \hbar}}

\displaystyle i \hbar \frac{\partial\Psi}{\partial t}= \hat{H}\Psi = -\frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2}+\hat{V}\Psi

\displaystyle i \hbar \frac{\partial\Psi}{\partial t}=  \hbar a\Psi

\displaystyle -\frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2}=  \hbar a(\frac{\partial}{\partial x} (x \Psi))

\displaystyle -\frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2}=   a( \hbar-2x^2a m)\Psi

\displaystyle \hbar a\Psi = a( \hbar-2x^2a m)\Psi+V\Psi

\displaystyle V(x)=2a^2 mx^2

\displaystyle \left<x\right>=A^2\int_{-\infty}^\infty x e^{-\frac{2am x^2}{\hbar}}\,dx=0

\displaystyle \left<x^2\right>=A^2\int_{-\infty}^\infty x^2 e^{-\frac{2am x^2}{\hbar}}\,dx=-\frac{\hbar }{m}A^2\int_0^\infty (-\frac{2m x^2}{\hbar}) e^{-\frac{2am x^2}{\hbar}}\,dx

\displaystyle \left<x^2\right>=-\frac{\hbar }{m}A^2\frac{\partial}{\partial a}\sqrt{\frac{\pi \hbar}{2ma}}=\frac{\hbar }{2ma}A^2\sqrt{\frac{\pi \hbar}{2ma}}

\displaystyle \left<p\right>=\frac{A^2\hbar}{2i}\int_{-\infty}^\infty (-\frac{4ma x}{\hbar}) e^{-\frac{2am x^2}{\hbar}}\,dx=0

\displaystyle \left< p^2\right>=-A^2\hbar^2\int_{-\infty}^\infty e^{-\frac{am x^2}{\hbar}}\frac{\partial}{\partial x}\left[ (-\frac{2ma x}{\hbar}) e^{-\frac{am x^2}{\hbar}}\right]\,dx

\displaystyle \left< p^2\right>=2A^2\hbar^2\int_0^\infty  {\left( -\frac{2ma x}{\hbar}\right)}^2 e^{-\frac{2am x^2}{\hbar}}\,dx

\displaystyle \left< p^2\right>=2A^2\hbar^2\sqrt{\frac{2ma }{\hbar}}\int_0^\infty  y^2 e^{-y^2}\,dy

\displaystyle \left< p^2\right>=-A^2\hbar^2\sqrt{\frac{2ma }{\hbar}}\int_0^\infty y (-2y) e^{-y^2}\,dy

\displaystyle \left<p\right>=A^2\hbar^2\sqrt{\frac{2ma }{\hbar}}\int_0^\infty e^{-y^2}\,dy

\displaystyle \left<p\right>=A^2\hbar^2\sqrt{\frac{2ma }{\hbar}}\sqrt{\pi\int_0^\infty e^{-\rho^2}2\rho\,d\rho}=A^2\hbar^2\sqrt{\frac{2\pi ma }{\hbar}}

\displaystyle \sigma_p^2 \sigma_x^2=A^2\hbar^2\sqrt{\frac{2\pi ma }{\hbar}}\frac{\hbar }{2ma}A^2\sqrt{\frac{\pi \hbar}{2ma}}=A^4\hbar^2\pi\frac{\hbar }{2ma}=\frac{\hbar^2}{4}

Linear algebraic group

Linear algebraic group

From Wikipedia, the free encyclopedia

In mathematics, a linear algebraic group is a subgroup of the group of invertible n×n matrices
(under matrix multiplication) that is defined by polynomial equations.

An exa…

Linear algebraic group

From Wikipedia, the free encyclopedia

In mathematics, a linear algebraic group is a subgroup of the group of invertible n×n matrices
(under matrix multiplication) that is defined by polynomial equations.

An example is the orthogonal group, defined by the relation MTM = I where MT is the transpose of
M.

http://en.wikipedia.org/wiki/Linear_algebraic_group

Las patronas

Video: Inmigrantes como moscas – Videos en ELPAÍS.comwww.elpais.comCada año unos 400.000 emigrantes centroamericanos intentan llegar a Estados Unidos, cruzando México. Viajan como moscas, sobre trenes de carga: No hay vuelos para los ilegales, ni fu…

Video: Inmigrantes como moscas – Videos en ELPAÍS.comwww.elpais.comCada año unos 400.000 emigrantes centroamericanos intentan llegar a Estados Unidos, cruzando México. Viajan como moscas, sobre trenes de carga: No hay vuelos para los ilegales, ni futuro… En un punto de Veracruz, encuentran una pequeña esperanza:


flops in Matlab

Somebody asked how one may count the number of floating point operations in a MATLAB program.
Prior to version 6, one used to be able to do this with the command flops, but this command is no longer available with the newer versions of MATLAB.
flops is a relic from the LINPACK days of MATLAB (LINPACK has since been replaced by LAPACK). With the use of LAPACK in MATLAB, it will be more

Somebody asked how one may count the number of floating point operations in a MATLAB program.
Prior to version 6, one used to be able to do this with the command flops, but this command is no longer available with the newer versions of MATLAB.
flops is a relic from the LINPACK days of MATLAB (LINPACK has since been replaced by LAPACK). With the use of LAPACK in MATLAB, it will be more

Lista de pendientes

Juega más juegos que el año pasado,
Lee más libros que el año pasado.

Mira al cielo al menos una vez al día,
date cuenta de la majestuosidad del mundo que te rodea.

Sueña más mientras estás despierto.

Come más alimentos que crezcan en el …

Juega más juegos que el año pasado,
Lee más libros que el año pasado.

Mira al cielo al menos una vez al día,
date cuenta de la majestuosidad del mundo que te rodea.

Sueña más mientras estás despierto.

Come más alimentos que crezcan en el campo
y menos alimentos que sean manufacturados en plantas industriales
o que requieran un sacrificio.

Come arándanos y nueces.
Toma té verde, mucha


Epistola

SOBRE LAS GUERRAS

(Parte 2 de las 4 que conforman la carta primera del SubMarcos a Don Luis Villoro, inicio del intercambio epistolar sobre Ética y Política. Enero-Febrero del 2011).

Como pueblos originarios mexicanos y como EZLN algo podemos decir…

SOBRE LAS GUERRAS

(Parte 2 de las 4 que conforman la carta primera del SubMarcos a Don Luis Villoro, inicio del intercambio epistolar sobre Ética y Política. Enero-Febrero del 2011).

Como pueblos originarios mexicanos y como EZLN algo podemos decir sobre la guerra. Sobre todo si se libra en nuestra geografía y en este calendario: México, inicios del siglo XXI…

II.- LA GUERRA DEL MÉXICO DE