As we know $I A=A$, where $A$ is a two dimensional matrix of order n and $I$ is the two dimensional identity matrix of order n, which contains 1 as diagonal positions and zero otherwise.
If we extend this concept to the case of 4-dimension, then how we explicitly express the corresponding Identity matrix ?
The identity square matrix is that with 1s on the main diagonal and 0s elswhere.
https://en.wikipedia.org/wiki/Identity_matrix
I do not understand exactly your question Dr Baliarsingh. All I can say, that the kronecker tensor product can allow to unedergo from 1D to 2D and 3D. The matlab command is kron. You can see the help on mathworks, on the following link :
http://www.mathworks.com/help/matlab/ref/kron.html
Best regards.
Thanks Prof. Kaddeche.
We know a explicitly how two dimensional identity matrix can be written. But in case of four dimension, how we write the identity matrix I (I=( i_{mnkl})) such that for any matrix A (A=( a_{mnkl})), we have
AI=IA=A.
I think Dr Viera is right. The identity matrix contains ones on the main diagonal and zeros elsewhere whatever it is 1D, 2D, 3d or even 4D. Only the size od the matrix will grow with the dimension of the treared problem.
Best regards.
In a four dimensional matrix, each element will be a matrix of 2D. If we take the Identity matrix of 4D, then it is too difficult to rearrange (may be possible) the element of the matrix such that upon multiplication of any 4D matrix to it has no effect on second matrix.
Dear Cernanova,
I have checked that the matrix given by you is satisfied AI=A. Also, we have an other matrix such that AI=A. Find the attachment (check for validity)
Dear colleague, the matrix A in your example is particular: all "submatrices" are the same. Therefore a matrix Q other than the identity matrix I and such that AQ=A can exist.
Can we conclude that the identity matrix for 4-D matrices can not be unique ?
In the Example that you proposed before you consider a special matrix A. It is not a general matrix. Thus it does not allow a general conclusion.
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