Gauss-Jordan Elimination, Rank and Singularity

The identity matrix is a speeial matrix with all elements being zero, except for the diagonal 

In MATLAB this matrix can easily be created by the eye command / = eye(3)  

Any matrix that is multiplied by the identity matrix yields the original matrix again, i.e. 

Vectors are orthogonal if their inner product is zero. Geometrically, this can be interpreted that the vectors have right angles to each other or perpendicular. Vectors are orthonormal if they are orthogonal and of unit length, in other words, the iimer product with themselves is unity. For an orthonormal set of column vectors v i = 1. , it should hold that  

An example of an orthonormal set is our coordinate system, consisting of three vectors at right angles of each other. In principal component analysis it will be shown that there ate other coordinate systems that are more convenient to use. 

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