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TimChan

Ttake you a few minutes

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i am wondering this matrix equation: setting F is a 4x4 matrix, M is a 3x3 transformation matrix, T is a translation vector and their inverses are bolded. FF = [ M | T ][ M | -MT ] [ 0 | 1 ][ 0 | 1 ] = [ MM | M(-MT)+T ]* [ 0 | 1 ] = [ I | 0 ] [ 0 | 1 ] = I *: Why this equation isn't [ MM | 0 ] but M(-MT)+T instead? [ 0 | 1 ] I would also like to ask if M/M is equivalent to M. Thank you=)

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[ M | T ][ M-1 | -M-1T ]
[ 0 | 1 ][ 0 | 1 ]
=
[ M*M-1 + T*0 | M*(-M-1T) + T*1 ]
[ 0*M-1 + 1*0 | 0*(-M-1T) + 1*1 ]
=
[ MM-1 | M(-M-1T) + T ]
[ 0 | 1 ]
=
[ I | -(MM-1)T + T ]
[ 0 | 1 ]
Is that what you need to know?

If 1/M = M-1, then M/M-1 = M(M-1)-1 = M2

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