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Contents1 Singular Value Decomposition (SVD) Singular Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular Value Decomposition (SVD) . . . . . . . . . . . . . . . . . . . . . Best RankkApproximations . . . . . . . . . . . . . . . . . . . . . . . . . Power Method for Computing the Singular Value Decomposition . . . . . . Applications of Singular Value Decomposition . . . . . . . . . . . . . . . . Component Analysis.

unit vector along this line. The length of the projection of a i;the ith row of A, onto v is ja i vj:From this we see that the sum of length squared of the projections is jAvj2.The best t line is the one maximizing jAvj2 and hence minimizing the sum of the squared distances of the points to the line.