Matrix forms of isometries

Matrix forms of isometries - Matrix forms of Isometries We...

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Matrix forms of Isometries We know that ( x,y ) a b c d ! = ( ax + cy,bx + dy ) . cos θ sin θ - sin θ cos θ ! : Counterclockwise rotation about the origin through θ. - 1 0 0 1 ! : Reflection about the y-axis. 1 0 0 - 1 ! : Reflection about the x-axis. 0 1 1 0 ! : Reflection about the line y = x . - 1 0 0 - 1 ! : Counterclockwise rotation about the origin through π 0 1 - 1 0 ! : Counterclockwise rotation about the origin through π/ 2 Matrix multiplication can also be used to determine the composition of two isometries which are given by matrices. For example we can evaluate ρ O,π/ 2 ρ O,π as follows : - 1 0 0 - 1 ! 0 1 - 1 0 ! . As we can see so as to evaluate
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