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I am having a hard time understanding how matrix works.

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Caleb Banga
Caleb Banga 2022-2-22
评论： Stephen23 2022-2-26
a = [ 1 0; 2 1] ;
b= [ -1 2 ; 0 1] ;
n= a*b
N= a.*b
what is the mathematical differnce between a.*b and a*b.

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回答（3 个）

Jan
Jan 2022-2-22
编辑：Jan 2022-2-26
.* is the elementwise multiplication, while * is the matrix multiplication:
[a,b; c,d] .* [e,f; g,h] =
[a*e, b*f; c*g, d*h]
[a,b; c,d] * [e,f; g,h] = % [EDITED, typos fixed]
[a*e + b*g, a*f + b*h; c*e + d*g, c*f + d*h]
See: https://en.wikipedia.org/wiki/Matrix_multiplication
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Walter Roberson
Walter Roberson 2022-2-26
编辑：Walter Roberson 2022-2-26
Jan, if the forum will run symbolic toolbox code for you then you are authorized to use the toolbox within the context of the forum; it is a service being provided by Mathworks.
It has the usual 55 second limit, and only about 5 gigabytes of ram, is about half the speed of your desktop, debugger and interactive input is disabled...
Stephen23
Stephen23 2022-2-26
@Jan: my pleasure! I also spent ten minutes trying to catch those flies, going through the steps of multiplying: however I am slow and those tiny flies are hard to catch. It was only when I was about to post the comment that it occured to me to try the symbolic toolbox, which luckily gave the same result :)

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Walter Roberson
Walter Roberson 2022-2-22
The operator .* is element-by-element multiplication. N = a.*b means that N(J,K) = a(J,K) times b(J,K) with no other elements of a or b influencing the outcome.
The operator * is algebraic matrix multiplication, also known as "inner product". n = a*b means that n(J,K) = dot(a(J,:), b(:,K)) which is an operation that involves a complete row of one matrix and a complete column of the other matrix. Carefully chosen matrix multiplication can express rotation, translation, and scale
Arthur Reis
Arthur Reis 2022-2-22
编辑：Arthur Reis 2022-2-22
'*' is the matrix multiplication as is usual in Linear Algebra
'.*' is element-wise multiplication. Each element is multiplied by its correspondent

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