Find $\|\mathbf{v}\|$ and $\|\mathbf{v+u}\|$ knowing $\|\mathbf{u}\|=3$; $\angle (\mathbf{u,v})=\frac{\pi}{4}$;$\angle (\mathbf{u+v,u})=\frac{\pi}{6}$

score 95 · Answer 12 · 2026-04-15 11:51:41

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Let $T$ be a linear operator in a vector space $V$ such as $T$ admits an ajoint. Prove that if $T^*T=0$ then $T=0$.

Published on 15 Apr 2026 - 11:51

score 64 · Answer 13 · 2026-04-17 13:12:37

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Which unit vector $\vec x$ maximises $\langle A\vec x|\vec x\rangle$?

Published on 17 Apr 2026 - 13:12

score 132 · Answer 14 · 2026-04-10 08:04:10

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John von Neumann - Norm induced by scalar product

Published on 10 Apr 2026 - 8:04

score 69 · Answer 15 · 2026-04-15 18:10:52

For which $\alpha, \beta \in \mathbb{R} $ is $\langle v,w \rangle = \alpha \langle v,w \rangle_1 + \beta \langle v,w \rangle_2$ an inner product?

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Find $\|\mathbf{v}\|$ and $\|\mathbf{v+u}\|$ knowing $\|\mathbf{u}\|=3$; $\angle (\mathbf{u,v})=\frac{\pi}{4}$;$\angle (\mathbf{u+v,u})=\frac{\pi}{6}$

Let $T$ be a linear operator in a vector space $V$ such as $T$ admits an ajoint. Prove that if $T^*T=0$ then $T=0$.

Which unit vector $\vec x$ maximises $\langle A\vec x|\vec x\rangle$?

John von Neumann - Norm induced by scalar product

For which $\alpha, \beta \in \mathbb{R} $ is $\langle v,w \rangle = \alpha \langle v,w \rangle_1 + \beta \langle v,w \rangle_2$ an inner product?

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