What is the group operation??

Steven G

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Dec 30, 2014
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If I multiply or add two matrices of this form I do not get back a matrix of the form! So what can the operation be?
I am assuming that the missing value can be any value.
What gives?
 
Of course I mean what can the operation of G' be?

I have been informed that blank spaces represent 0. Is this common notation?
 
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