Re: Matrix decomposition in vectors

"Umair Mansoor" <umairbinmansoor@xxxxxxxxxxx> wrote in message <glnect$80d$1@xxxxxxxxxxxxxxxxxx>...
"John D'Errico" <woodchips@xxxxxxxxxxxxxxxx> wrote in message <glknao$qv$1@xxxxxxxxxxxxxxxxxx>...
"Umair Mansoor" <umairbinmansoor@xxxxxxxxxxx> wrote in message <glkkq2$8i2$1@xxxxxxxxxxxxxxxxxx>...
Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?

In general, this is impossible, unless the 2x2 matrix
is singular. For higher dimensioned matrices, the
matrix must be rank 1 to be decomposed in this way.

So is your 2x2 matrix singular? I.e., is it a rank 1 matrix?

John

I just know that its symmetric

If that is all you know, then it is impossible
in general. It is not that we cannot find
such a pair of vectors. Rather, there do not
exist a pair of vectors such that this is true
for a general 2x2 symmetric matrix.

John
.

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