document.write( "Question 1165603: Suppose T : R2 → R2 is the transformation that reflects vectors across the line y = x. Find the eigenvalues and eigenvectors for this transformation. \n" ); document.write( "

Algebra.Com's Answer #790085 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "This transformation leaves UNCHEANGABLE the vectors  (x,y)  in the plane with x=y\r\n" );
document.write( "\r\n" );
document.write( "that lie on the line  y=x.  \r\n" );
document.write( "\r\n" );
document.write( "Hence, these vectors  (x,x)  are eigenvectors with the eigenvalue of 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This transformation CHANGEs the vectors  (x,y)  in the plane with x=-y\r\n" );
document.write( "\r\n" );
document.write( "that lie on the line  y=-x,  orthogonal to the line  x=y.  \r\n" );
document.write( "\r\n" );
document.write( "The transformation transforms each such a vector into the opposite one.\r\n" );
document.write( "\r\n" );
document.write( "Hence, these vectors  (x,-x) are eigenvectors with the eigenvalue of -1.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );