Meaning of the symbol '' \ ''

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Waqas Syed
Waqas Syed 2015-7-28
编辑： Bruno Luong 2021-10-1
Hi,
I am trying to understand a pre written matlab code. There is a line: dx = -(J \ F);
What does the forward slash mean? Does it mean F divided by J or something?

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Lukas Bystricky
Lukas Bystricky 2015-7-28
编辑：Lukas Bystricky 2015-7-28
That's actually a backward slash. J\F is equivalent to solving the system J dx = F for dx, where J is a matrix (probably a Jacobian) and F and dx are vectors.
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Bruno Luong
Bruno Luong 2021-10-1
Ran in:
@Walter Roberson: "So J\F vs F/J would only be the same if F and J are each real and symmetric."
Not true
J=rand(3); J=J+J',
J = 3×3
0.0670 0.8628 0.2369 0.8628 1.6893 1.1714 0.2369 1.1714 1.6260
F=rand(3); F=F+F',
F = 3×3
0.8988 0.3888 0.1346 0.3888 0.2691 0.9150 0.1346 0.9150 1.4615
J\F
ans = 3×3
-1.1987 -1.0761 -0.0648 1.3265 0.4196 -0.1101 -0.6982 0.4172 0.9877
F/J
ans = 3×3
-1.1987 1.3265 -0.6982 -1.0761 0.4196 0.4172 -0.0648 -0.1101 0.9877
Bruno Luong
Bruno Luong 2021-10-1
编辑：Bruno Luong 2021-10-1
@Kriti Salwan "What happens if we are applying backlash to a matrix which is not square ?"
x = A\b;
For A with rank(A) < size(A,2) see https://blogs.mathworks.com/cleve/2021/04/28/solving-commodious-linear-systems/
Otherwise it's a least square solution
x = argmin(norm(A*x-b))
or equivalently
x = pinv(A)*b

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