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Whether $SO_k(\mathbb{Q})\subsetneq SO_k(\mathbb{Q(\sqrt{n})})$

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#linear-algebra #number-theory #field-theory #orthogonal-matrices
108
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General question about Self-adjoint operators on Hilbert Spaces

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#real-analysis #linear-algebra #functional-analysis
199
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Determination of all invariant subspaces

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#linear-algebra #linear-transformations
57
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Equivalence between the SDP and the given problem

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#linear-algebra #matrices #semidefinite-programming
370
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Axler 3rd Theorem 3.60 Prove that L(V,W) is isomorphic to F^{m,n}

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#linear-algebra #vector-spaces #vector-space-isomorphism
194
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Topological property of preimage of map $f$ taking the coefficients of characteristic polynomial?

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#linear-algebra #general-topology #polynomials #connectedness #path-connected
474
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Row versus column picture

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#linear-algebra #visualization
71
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Is $Q + A$ postive semidefinte?

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#linear-algebra
888
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Can an upper triangular matrix be put in jordan form using upper triangular matrices and permutations only.

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#linear-algebra
106
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Linear Algebra Column and Null Spaces

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#linear-algebra #matrices #vector-spaces
298
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Finding the pattern to a general matrix

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#linear-algebra #eigenvalues-eigenvectors #determinant
195
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Proof that -1 can't be an eigenvalue

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#linear-algebra #graph-theory
451
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Two non-parallel, coplanar lines in $\mathbb{R}^n$ must intersect

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#linear-algebra #analytic-geometry
48
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then find the matrix $ \ A' \ $ with respect to the basis $ \ B'=\{(-2,1), \ (-1,1) \} \ $

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#linear-algebra
1.3k
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Is $A^TBA$ positive definite if and only if $A$ is nonsingular and $B$ is positive definite

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#linear-algebra #proof-verification #matrix-equations #positive-definite

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