transformation matrices rotation matrices to rotate a vector we use a rotation matrix for example consider the vector plotvectors let s rotate this vector by 80 degrees or 80 180 ...
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...Transformation matrices rotation to rotate a vector we use matrix for example consider the plotvectors let s this by degrees or radians r convenience matlab has function degrad that converts between and there also raddeg convert from ans pi properties of columns are orthogonal magnitude each column is one trigonometric identity if unit then an implies inverse simply its transpose ve defined in counter clockwise direction must apply same since translation what want translate i e move it some distances such answer no affine shift so cannot define using strictly linear operator however can perform translations d space add third dummy dimension write our as giving value now where notice how regenerates last entry allows us transformations but entries never changed combining multiplication sequential operations first need make them compatible with bottom right corner new still have thus both dimensions two analyzing linkage systems common problem robotics finding position end arm multiplie ...