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.
- Sextillion
- Sexy Primes
- Seydewitz's Theorem
- Sgn
- Shadow
- Shadowing Theorem
- Shafarevich Conjecture
- Shah Function
- Shah-Wilson Constant
- Shallit Constant
- Shallow Diagonal
- Shanks' Algorithm
- Shanks' Conjecture
- Shannon Entropy
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- Shape Operator
- Shapiro's Cyclic Sum Constant
- Sharing Problem
- Sharkovsky's Theorem
- Sharpe Ratio
- Sharpe's Differential Equation
- Sheaf (Geometry)
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- Shear
- Shear Matrix