rank of complex matrix over the real field

hedipaldi

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Aug 26, 2015
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consider the foloiwing 2x2 matrix in the vector space of 2x2 complex matrices over the real field:
1 2
i 2i

the rows are linearly independent over the real field,but the columns are linearly dependent.
so the row rank is 2 while the column rank is 1.
how come?
 
consider the foloiwing 2x2 matrix in the vector space of 2x2 complex matrices over the real field:

\(\displaystyle \left[\, \begin{array}{cc}1&2\\i&2i \end{array}\, \right]\)

the rows are linearly independent over the real field,but the columns are linearly dependent.
so the row rank is 2 while the column rank is 1.
how come?
Um... "How come" what? Or are you saying that some portion of your post (previous to the "how come") consists of the statements of somebody else (such as your textbook or something from your class notes)?

Please be specific. Thank you! ;)
 
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