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what does A/b mean when solving matrix Ax=b

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Marisa
Marisa 2023-12-11
回答： Walter Roberson 2023-12-11
A/b

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回答（3 个）

Steven Lord
Steven Lord 2023-12-11
The \ operator (mldivide function) solves for x in A*x = b.
The / operator (mrdivide function) solves for x in x*A = b.
Voss
Voss 2023-12-11
Walter Roberson
Walter Roberson 2023-12-11
If you have A*x = b then x = A\b is very likely what you need
But if for some reason you want to know what meaning A/b would have in that situation, then:
If A*x = b then A*x*pinv(x) ~~ b*pinv(x) . But A*x*pinv(x) ~~ A because x*pinv(x) ~~ identity matrix. So A*x*pinv(x) ~~ b*pinv(x) ==> A ~~ b*pinv(x) .
Now right-mutiply both sides by pinv(b) to get A*pinv(b) ~~ b*pinv(x)*pinv(b)
Now A*pinv(b) is expressible in MATLAB as A/b, so A/b ~~ b*pinv(x)*pinv(b)
Unfortunately for unknown x that does not get you anywhere useful... except that there are some restricted cases in which pinv(x)*pinv(b) == pinv(b)*pinv(x) and if you just happened to fall into one of those then A/b ~~ pinv(x)
But in practice there is seldom a useful relationship between A/b and A\b. Most of the time you cannot even do both operations due to the restrictions on the column dimensions that \ and / have.
There are however relationships between the operators. According to the Tips,
The operators / and \ are related to each other by the equation B/A = (A'\B')'

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