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Questions tagged [linear-algebra]

Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically concerning matrices, use the (matrices) tag. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

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On an inequality involving operator norm of matrices and singular value

Let $A, E \in M_n(\mathbb C)$ be as in this question On invertibility of $A+E$ where $||E||_2<$ smallest singular value of $A$ and $||A^{-1}E||_2<1$ . How to prove that $\dfrac {||A^{-1}b-(A+E)...
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Computing the logarithm of an exponentiated matrix?

Let $\mathfrak{g} \subseteq \mathfrak{su}(n)$ be a linear Lie algebra represented by skew-symmetric $n\times n$ matrices. Let $C \in SU(n)$ be a special unitary matrix where it is known that $C = exp\{...
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Showing equivalence of set of solutions of two linear programming

Setup of the problem (updated thanks to comments below) Consider six finite sets of real numbers each with cardinality $4$ $$ \mathcal{A}\equiv \{a_1,a_2,a_3,a_4\}\text{, }\text{ }\tilde{\mathcal{A}}\...
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Proving generating system for $U:=\{(a,b,c,d)|a+b+c+d=0)\},U\subseteq \mathbb{C}^4=:V,V\mathbb{R}$-vectorspace

I have already proved it if V would be a $\mathbb{C}$ vectorspace. I picked $(1,-1,0,0);(0,1,-1,0);(0,0,1,-1)$ as my base showed linear Independence and said if there would exist one more basevector ...