Matrix Decomposition Theorem
Let 
be a Matrix of Eigenvectors of a given Matrix 
and 
aMatrix of the corresponding Eigenvalues. Then can be written
 | (1) |
is a Diagonal Matrix and the columns of are Orthogonal Vectors. If is not aSquare Matrix, then it cannot have a Matrix Inverse. However, if P is 
(with 
), then can be written using a so-called Singular Value Decomposition of the form | (2) |
and 
are 
Square Matrices with Orthogonal columns, | (3) |
References
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Singular Value Decomposition.'' §2.6 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 51-63, 1992.
- Ramanujan's Square Equation
- Ramanujan's Sum
- Ramanujan's Sum Identity
- Ramanujan's Tau-Dirichlet Series
- Ramanujan's Tau Function
- Ramanujan Theta Functions
- Ramp Function
- Ramphoid Cusp
- Ramsey Number
- Ramsey's Theorem
- Randelbrot Set
- Random Distribution
- Random Dot Stereogram
- Random Graph
- Random Matrix
- Random Number
- Random Percolation
- Random Polynomial
- Random Variable
- Random Walk
- Random Walk--1-D
- Random Walk--2-D
- Random Walk--3-D
- Range (Image)
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