| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
I have the following question on linear independence.
Let f(.) be a function which is strictly monotonic, continuous, and
a first and third quadrant non-linearity, i.e. x f(x) > 0 for
all x != 0 and f(x) = 0 for x =0. Also
|f(x)| |f(y)|
------ <= ------ for all |x| >= |y|
|x| |y|
Now, let the columns of a matrix X with elements x_{i,j} be linearly
independent. Will the columns of the matrix F with elements
f(x_{i,j}) be linearly independent?
Curiously,
S. Sudharsanan
pasta::sudharsanan
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1851.1 | Counterexample | WIBBIN::NOYCE | DEC 21064-200DX5 : 130 SPECint @ $36K | Mon Mar 14 1994 10:39 | 3 |
[ 3 4 ] [ 3 4 ]
No. Given X = [ ] we could have F = [ ]
[ 6 10 ] [ 6 8 ]
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| 1851.2 | More Restrictions on the function | PASTA::SUDHARSANAN | Mon Mar 14 1994 12:51 | 18 | |
re.1
I can actually further restrict my function f(.) as follows,
|f(x)| |f(y)|
------ < ------
|x| |y|
for all |x| > |y|.
Also, I can impose the condition that f(.) be a C-infinity function,
i.e. it is continuously differentiable infinitely many times.
The above restrictions will make the counterexample invalid, however
the claim in the original note may still not be true.
S. Sudharsanan
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