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In the case of vectors we can form a matrix with columns as those vectors and find the reduced-row echelon form. A basis can be easily written from the given spanning vectors by looking at the pivotal rows of the reduced matrix.

But, is there a similar method if we are given spanning matrices? How to form the basis matrices of the space spanned by some given matrices?

Any hints are welcome and thanks in advance.

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  • $\begingroup$ A 2 by 2 matrix is a 4 dimensional object... $\endgroup$ – Paul Nov 5 '16 at 20:00
  • $\begingroup$ Sir, Since a 2*2 matrix has four independent terms it is an element of a 4-D vector space. But, I didn't understand your hint regarding this question. $\endgroup$ – Rajath Krishna R Nov 5 '16 at 20:08
  • $\begingroup$ @RajathKrishnaR A space of matrices is isomorphic to a space of column vectors. Do the work in your space of column vectors and then apply the isomorphism. $\endgroup$ – Jacob Wakem Nov 5 '16 at 20:33
  • $\begingroup$ ohh...yes!! Ok. thank you so much. $\endgroup$ – Rajath Krishna R Nov 5 '16 at 20:39

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