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Suplemento de Matrix
En matemáticas, la adición de matrices es la operación de agregar dos matrices agregando las entradas correspondientes.
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Matrix addition
From Wikipedia, the free encyclopedia
(Redirected from Matrix subtraction )
Illustration of the addition of two matrices.
Notions of sums for matrices in linear algebra
In mathematics , matrix addition is the operation of adding two matrices by adding the corresponding entries together.
For a vector ,
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{\displaystyle \mathbf {A} {\vec {v}}+\mathbf {B} {\vec {v}}=(\mathbf {A} +\mathbf {B} ){\vec {v}}\!}
Two matrices must have an equal number of rows and columns to be added.[ 1] A and B will be a matrix which has the same number of rows and columns as A and B . The sum of A and B , denoted A + B A and B :
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{\displaystyle {\begin{aligned}\mathbf {A} +\mathbf {B} &={\begin{bmatrix}a_{11}&a_{12}&\cdots &a_{1n}\\a_{21}&a_{22}&\cdots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}&a_{m2}&\cdots &a_{mn}\\\end{bmatrix}}+{\begin{bmatrix}b_{11}&b_{12}&\cdots &b_{1n}\\b_{21}&b_{22}&\cdots &b_{2n}\\\vdots &\vdots &\ddots &\vdots \\b_{m1}&b_{m2}&\cdots &b_{mn}\\\end{bmatrix}}\\&={\begin{bmatrix}a_{11}+b_{11}&a_{12}+b_{12}&\cdots &a_{1n}+b_{1n}\\a_{21}+b_{21}&a_{22}+b_{22}&\cdots &a_{2n}+b_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}+b_{m1}&a_{m2}+b_{m2}&\cdots &a_{mn}+b_{mn}\\\end{bmatrix}}\\\end{aligned}}\,\!}
Or more concisely (assuming that A + B = C [ 4]
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{\displaystyle c_{ij}=a_{ij}+b_{ij}}
For example:
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{\displaystyle {\begin{bmatrix}1&3\\1&0\\1&2\end{bmatrix}}+{\begin{bmatrix}0&0\\7&5\\2&1\end{bmatrix}}={\begin{bmatrix}1+0&3+0\\1+7&0+5\\1+2&2+1\end{bmatrix}}={\begin{bmatrix}1&3\\8&5\\3&3\end{bmatrix}}}
Similarly, it is also possible to subtract one matrix from another, as long as they have the same dimensions. The difference of A and B , denoted A − B B from corresponding elements of A , and has the same dimensions as A and B . For example:
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{\displaystyle {\begin{bmatrix}1&3\\1&0\\1&2\end{bmatrix}}-{\begin{bmatrix}0&0\\7&5\\2&1\end{bmatrix}}={\begin{bmatrix}1-0&3-0\\1-7&0-5\\1-2&2-1\end{bmatrix}}={\begin{bmatrix}1&3\\-6&-5\\-1&1\end{bmatrix}}}
↑ Elementary Linear Algebra by Rorres Anton 10e p53 ↑ Weisstein, Eric W. "Matrix Addition" . mathworld.wolfram.com . Retrieved 2020-09-07 .
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