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Let M be a column vector (not null vecto...

Let M be a column vector (not null vector) and `A=(MM^T)/(M^TM)` the matrix A is : (where `M^T` is transpose matrix of M)

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`A=(m*m^T)/(m^Tm)`
`mmT=[[a],[b],[c]]_(3*1)*[a,b,c]_(1*3)`
`[[a^2,ab,ac],[ab,b^2,bc],[ac,bc,c^2]]_(3*3)`
`m^T*m=[a,b,c]_(1*3)[[a],[b],[c]]=[a^2+b^2+c^2]`
`A=1/(a^2+b^2+c^2)[[a^2,ab,ac],[ab,b^2,bc],[ac,bc,c^2]]`
`=(a^2b^2c^2+a^2b^2c^2+a^2b^2c^2)-(a^2b^2c^2+a^2b^2c^2+a^2b^2c^2)`
`A^m=0`.
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