document.write( "Question 1182571: Consider C as a vector space over itself. Let T : C → C be the function T(z) = ¯z. Is T a linear transformation? Justify your answer \n" ); document.write( "

Algebra.Com's Answer #812647 by ikleyn(52858) $\"\"$ $\"About$

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document.write( "Although the map T transfers the sum of vectors (of complex numbers, in this case) to the sum,\r\n" );
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document.write( "the axiom of the linear transformation fails for the multiplication by the number.\r\n" );
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document.write( "Indeed, according to the axiom, it should be\r\n" );
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document.write( "    T(cz) = c*¯z,     (1)\r\n" );
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document.write( "but in reality\r\n" );
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document.write( "    ¯(cz) = ¯c*¯z,    (2)\r\n" );
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document.write( "which is DIFFERENT from  (1).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus the map T IS NOT a linear transformation in this case.\r
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