For vecor space $V$, prove there exists $\{ u_1, \cdots , u_n \} \subset V$ s.t. $(a_i, u_j)=\delta_{ij}$ where $\{ a_1, \cdots , a_n \} $ is a basis.

score 45 · Answer 14 · 2026-04-15 10:39:01

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Range of values for $\frac{\langle f | \mathbf n \cdot \boldsymbol \sigma |f \rangle}{\langle f | f \rangle}$, with $|\mathbf n| = 1$?

Published on 15 Apr 2026 - 10:39

score 58 · Answer 15 · 2026-04-13 21:46:00

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What is the dot product between these two vectors?

Published on 13 Apr 2026 - 21:46

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For vecor space $V$, prove there exists $\{ u_1, \cdots , u_n \} \subset V$ s.t. $(a_i, u_j)=\delta_{ij}$ where $\{ a_1, \cdots , a_n \} $ is a basis.

Range of values for $\frac{\langle f | \mathbf n \cdot \boldsymbol \sigma |f \rangle}{\langle f | f \rangle}$, with $|\mathbf n| = 1$?

What is the dot product between these two vectors?

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