List questions from inner-products

Published on 13 Apr 2026 - 15:39

172

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Orthogonality on complex inner product space

Published on 14 Apr 2026 - 11:42

104

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Is continuous function space with standard inner product on $\big[0,\frac{1}{2}\big]$ not complete?

Published on 14 Apr 2026 - 16:17

154

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$T: \mathbb R^n \to \mathbb R^n$, $\langle Tu,v\rangle=\langle u,T^v\rangle$, is $T^=T^t$ regardless of inner product?

Published on 14 Apr 2026 - 21:49

401

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Prove series converges absolutely

Published on 12 Apr 2026 - 17:46

7.8k

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Prove that set is orthonormal set

Published on 13 Apr 2026 - 21:34

261

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Matrix Composed of Traces of Linear Independent Set of Matrices

Published on 12 Apr 2026 - 4:06

2k

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Is any norm induced by some inner product?

Published on 11 Apr 2026 - 4:01

312

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Inner product question

Published on 12 Apr 2026 - 0:42

5.8k

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$T^T=TT^$ and $T^2=T$. Prove $T$ is self adjoint: $T=T^*$

Published on 17 Apr 2026 - 4:05

542

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Show a linear transform is self adjoint - check my answer

Published on 15 Apr 2026 - 17:35

59

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For inner product spaces, do we have $||\vec{u}-\vec{v}|| \leq ||\vec{u}||+||\vec{v}||$?

Published on 15 Apr 2026 - 16:05

93

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Distribution Property of Dot Product

Published on 12 Apr 2026 - 7:45

114

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Homework: Second derivative of $\langle Ax, x \rangle$

Published on 14 Apr 2026 - 6:59

201

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Prove $\langle x,x \rangle < 0$ or $\langle x,x \rangle > 0$ for all $x \neq 0$

Published on 17 Apr 2026 - 15:59

List Question

On the completeness of inner product spaces.

Orthogonality on complex inner product space

Is continuous function space with standard inner product on $\big[0,\frac{1}{2}\big]$ not complete?

$T: \mathbb R^n \to \mathbb R^n$, $\langle Tu,v\rangle=\langle u,T^v\rangle$, is $T^=T^t$ regardless of inner product?

Prove series converges absolutely

Prove that set is orthonormal set

Matrix Composed of Traces of Linear Independent Set of Matrices

Is any norm induced by some inner product?

Inner product question

$T^T=TT^$ and $T^2=T$. Prove $T$ is self adjoint: $T=T^*$

Show a linear transform is self adjoint - check my answer

For inner product spaces, do we have $||\vec{u}-\vec{v}|| \leq ||\vec{u}||+||\vec{v}||$?

Distribution Property of Dot Product

Homework: Second derivative of $\langle Ax, x \rangle$

Prove $\langle x,x \rangle < 0$ or $\langle x,x \rangle > 0$ for all $x \neq 0$

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