Matlab, operator A\B
What is the result of the operation A\B, where A(1, m) and B (1, m)?
In the manual it is written:
A\B returns a least-squares solution to the system of equations A*x= B.
So it means x = inv (A'*A)*A'*B? However, the matrix A'*A is singular...
Let us suppose:
A=[1 2 3] B=[6 7 6] A\B 0 0 0 0 0 0 2.0000 2.3333 2.0000 If ve use MLS: C = inv (A'*A) singular matrix C = pinv(A'*A) 0.0051 0.0102 0.0153 0.0102 0.0204 0.0306 0.0153 0.0306 0.0459 D= C*A'*B 0.4286 0.5000 0.4286 0.8571 1.0000 0.8571 1.2857 1.5000 1.2857
So results A\B and inv (A'*A)*A'*B are different...
NOTE:-
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My MATLAB (R2010b) says quite a lot about what
A\B
does:
mldivide(A,B)
and the equivalentA\B
perform matrix left division (back slash).A
andB
must be matrices that have the same number of rows, unlessA
is a scalar, in which caseA\B
performs element-wise division — that is,A\B = A.\B
.If
A
is a square matrix,A\B
is roughly the same asinv(A)*B
, except it is computed in a different way. IfA
is ann
-by-n
matrix andB
is a column vector withn
elements, or a matrix with several such columns, thenX = A\B
is the solution to the equationAX = B
. A warning message is displayed ifA
is badly scaled or nearly singular.If
A
is anm
-by-n
matrix withm ~= n
andB
is a column vector withm
components, or a matrix with several such columns, thenX = A\B
is the solution in the least squares sense toSEE COMPLETE ANSWER CLICK THE LINKhttps://matlabhelpers.com/questions/matlab-operator-a-b.php
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