how can i separate a matrix into a multiplication of two matrices One of Real Values and the Other for Integer values.

4 次查看（过去 30 天）
ahcen aliouat
ahcen aliouat 2019-7-8
编辑： Bruno Luong 2019-7-9
hello,
how can i separate a matrix X into a multiplication of two matrices Y and Z with Y contain Real Values and Z contain Integer values using MATLAB.
such as: X=Y*Z
with:
X= my Input Matrix of NxN.
and i search to obtain:
Y: matrix of integer values.
Z: Matrix of Real Values.
X is suposed to be a NxN matrix.

请先登录，再回答此问题。

采纳的回答

Bruno Luong
Bruno Luong 2019-7-8
编辑：Bruno Luong 2019-7-8
Of course.
Test matrix
X = rand(5)
n = length(X)
then
Z = ceil(1000*rand(n,n))
Y = X/Z
Y*Z
  3 个评论
显示 1更早的评论
ahcen aliouat
ahcen aliouat 2019-7-9
hello,
please @bruno could you give me an idea on how to get it in a way that the Real values matrix will be a diagonal matrix? ( identified just in the diagonal )
i will appreciate your help.
thank you
Bruno Luong
Bruno Luong 2019-7-9
编辑：Bruno Luong 2019-7-9
In general it's not possible for any X.
If you have such decompistion, it's equivalent to each column of X has a common divisor (on the diagonal of Z). And that is right for all column.
This condition is quite strict. But if you know X meets this, then you can write down:
X(:,j) = sum k_(i,j) d_j, for all j=1,2,...,n, with k_(i,j) integers
Then simply take
Z = diag(d)
Y(i,j) = k_(i,j)
You might try to apply euclidian algorithm to find a common divisor of floating points (if any), I'm not sure the bad-effect of floating points round-off on such algorithm (I guess it's far from robust).

请先登录，再进行评论。

更多回答（1 个）

Raj
Raj 2019-7-8
There are infinite combinations possible (atleast by theory) in which you can split a real number to multiplication of a real number and an integer. Let me explain:
X=rand(N,N) % your matrix
Y=randi(M,N) % any NxN integer matrix with upper limit as M. INFINITE Possibilities here.
then
Z=X./Y % matrix of real values.
So that you can multiply Y & Z to get back X
X1=Y.*Z
isequal(X,X1) % confirms that X and X1 are equal.
Cheers!!
  1 个评论
ahcen aliouat
ahcen aliouat 2019-7-9
thank you very much.
do you have an idea on how to get it in a way that the Real values matrix will be a diagonal matrix? ( identified just in the diagonal )
i will appreciate your help.
thank you

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Operating on Diagonal Matrices 的更多信息

标签

产品


版本

R2017b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by