List questions from inner-products

Published on 12 Apr 2026 - 21:17

69

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Let $A, B:V \to V$ be two linear operators in a vector space with inner product. If $A$ and $B$ commutes then so does $A^\ast$ and $B^\ast$

Published on 14 Apr 2026 - 19:46

764

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Bounding the sum of absolute values of an orthogonal matrix's entries

Published on 15 Apr 2026 - 9:08

51

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Need help proving $\langle u,v\rangle = 0$ iff $ \|u\| \le \|u+cv\|$ for all scalars $c$.

Published on 14 Apr 2026 - 23:59

129

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Proof that the adjoint operator of $\Phi$ is $\Phi(\sigma)=\sum_{i}A_{i}^{*}\sigma B_{i}$ in terms of Kraus operators.

Published on 11 Apr 2026 - 21:26

93

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Cardinality of Hamel basis of a separable incomplete inner product space

Published on 15 Apr 2026 - 10:07

23

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Bounding a Function When We Only Know Its Dot Product Against Test Functions.

Published on 24 Apr 2026 - 13:54

901

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$A$ and $B$ are positive self-adjoint matrix such that $AB$ is self-adjoint then $AB$ is positive

Published on 29 Mar 2026 - 3:37

1k

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Using Gram-Schmidt to find an orthonormal basis.

Published on 14 Apr 2026 - 11:06

327

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To show that $f$ is an orthogonal linear map, if $f(0) = 0$ and $f$ preserves the distance

Published on 16 Apr 2026 - 10:04

85

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All isometries $f:V\to V$ can be written as $f = T_u\circ A$ - proof of uniqueness?

Published on 14 Apr 2026 - 13:29

79

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Inner product matrix

Published on 12 Apr 2026 - 21:00

136

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Adjoint operator of a partial differential operator used to do the carleman estimate

Published on 28 Mar 2026 - 18:22

112

Views

Best approximation proof question

Published on 12 Apr 2026 - 4:46

53

Views

Proving inner product conditions.

Published on 09 Apr 2026 - 10:50

List Question

Inner (Dot) Product Inequality

Let $A, B:V \to V$ be two linear operators in a vector space with inner product. If $A$ and $B$ commutes then so does $A^\ast$ and $B^\ast$

Bounding the sum of absolute values of an orthogonal matrix's entries

Need help proving $\langle u,v\rangle = 0$ iff $ \|u\| \le \|u+cv\|$ for all scalars $c$.

Proof that the adjoint operator of $\Phi$ is $\Phi(\sigma)=\sum_{i}A_{i}^{*}\sigma B_{i}$ in terms of Kraus operators.

Cardinality of Hamel basis of a separable incomplete inner product space

Bounding a Function When We Only Know Its Dot Product Against Test Functions.

$A$ and $B$ are positive self-adjoint matrix such that $AB$ is self-adjoint then $AB$ is positive

Using Gram-Schmidt to find an orthonormal basis.

To show that $f$ is an orthogonal linear map, if $f(0) = 0$ and $f$ preserves the distance

All isometries $f:V\to V$ can be written as $f = T_u\circ A$ - proof of uniqueness?

Inner product matrix

Adjoint operator of a partial differential operator used to do the carleman estimate

Best approximation proof question

Proving inner product conditions.

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