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  • matrices - A book for self-study of matrix decompositions - Mathematics . . .
    It's got a great exposition of many matrix decompositions and how they are useful for numerical analysis (basically how to solve linear algebra problems in the real world) In particular it's got a great section on SVD, QR and Cholesky decompositions
  • linear algebra - Intuitively, what is the difference between . . .
    I'm trying to intuitively understand the difference between SVD and eigendecomposition From my understanding, eigendecomposition seeks to describe a linear transformation as a sequence of three ba
  • linear algebra - When does a matrix have a cyclic decomposition and . . .
    Cyclic decompositions lead to "rational forms"; special matrices similar to the original one over the the original field (no field extension) These forms exist whether or not the eigenvalues (characteristic values) live over the base field, since blocks of the matrix are companion matrices of the annihilators of the cyclic factors which could
  • linear algebra - Connections between two full rank decompositions . . .
    So now we know the structure of full rank decomposition clearly, although it may not be as useful as other decompositions However, it's still a good exercise for students who just contact linear algebra, as it only uses elementary method
  • Symmetric decompositions of $SU(2)$ representations.
    There is a general result saying that the weight vector with highest possible weight will always generate an irreducible subrepresentation, and there there is an invariant complement to this subrepresentation This allows you to compute decompositions in an elementary way Take the example of $\mathbf{3} \otimes \mathbf{3}$
  • Calculating polar decomposition - Mathematics Stack Exchange
    How do I compute the left and right polar decompositions of a matrix by hand? I understand the definition of the decomposition but not how it is calculated For instance are the left and right polar decompositions of this matrix different, and how do I compute them? $$ \begin{bmatrix} 2 -3\\ 1 6\\ \end{bmatrix} $$
  • Matrix decomposition definition - Mathematics Stack Exchange
    There are many different matrix decompositions; each finds use among a particular class of problems " But in my opinion decomposition term should be used to represent breaking a matrix in different sub-matrices or some new matrices created after some operation on original matrix which if used together and passed through some algorithm(not
  • reference request - Methods for finding decompositions of Hilbert . . .
    Well, I'm a physicist and these types of operators pop up everywhere, in my particular case it is the context of optics Hilbert-Schmidt decompositions are particularly useful due to the orthogonality of the modes, which is essential in statistical mechanics applications, inverse problems and few mode approximations (to only name a few)
  • Number of distinct decompositions - Mathematics Stack Exchange
    Number of distinct decompositions Ask Question Asked 11 years, 3 months ago Modified 11 years, 3 months ago





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