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Results tagged with matrix-theory
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user 4987
Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.
5
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almost diagonal Positive semidefinite Matrix
Consider the set $\mathcal{D}_n$ of $n$-dimensional positive semidefinite matrices.
A matrix $M\in \mathcal{D}_n$ is called $\epsilon$ diagonal in trace distance if there is a diagonal matrix $D\in \m …
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5
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0
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On the linear transformation between matrix space
Suppose we have two matrix subspaces, $n\times n$ matrix subspace $S_1$ and $m\times m$ matrix subspace $S_2$. Every element of $S_1$ and $S_2$ is complex symmetric matrix.
Suppose there exists matri …
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On the positivity of matrices
For given $n$, the following $n\times n$ real matrix $M=M^{T}$ is called positive, if
$x^{T}M x\geq 0$
holds for all non-negative real $x_1,x_2,\cdots,x_n$,
where $x=(x_1,x_2,\cdots,x_n)^T$.
Notic …
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2
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answer
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Primal identity in matrix semigroup
Given a finite set of matrix $\{M_1,M_2,\cdots,M_n\}\subseteq \mathbb{C}^{d\times d}$, we consider the semigroup generated by matrix product.
We call $s_1\cdots s_k$ an identity index if
$M_{s_1}M_{s_ …
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0
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Jordan Decomposition of Sparse matrix
Suppose we are given $n \times n$ rational matrix, $A$ with at most $k$ nonzero elements in each row and each column with $k \ll n$.
What is the best algorithm to compute its Jordan decomposition? Wh …
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