List questions from inner-products

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Exercise $3$, Section $6.A$ - Linear Algebra Done Right

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Dependency of the Hessian on the inner product

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Show that an inner product space is always strictly convex.

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Find the matrix maximizing a summation of bilinear forms

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Show $A \subset B \Leftrightarrow B^{\perp} \subset A^{\perp}$ with $A,B$ subsets of a Hilbert space.

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What do we measure using norm?

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The correct way to map a column vector into a row vector.

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What surface is represented by $\mathbf{r}\cdot\mathbf{a} = \mathrm{const.}$?

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How to get a vector from two points

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Bound on $|x \cdot y|$ from below

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Proof that an operator is self-adjoint if and only if its matrix is self-adjoint

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For a compact group $G$ and any finite-dimensional complex representation $(\pi,V)$, how to show that $V$ admits an invariant inner product?

Published on 08 Sep 2023 - 8:27

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Comparison of the expectation of minimums of random variables

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List Question

Does Hilbert $C^*$-modules have orthonormal basis?

Exercise $3$, Section $6.A$ - Linear Algebra Done Right

Dependency of the Hessian on the inner product

Show that an inner product space is always strictly convex.

Find the matrix maximizing a summation of bilinear forms

Show $A \subset B \Leftrightarrow B^{\perp} \subset A^{\perp}$ with $A,B$ subsets of a Hilbert space.

What do we measure using norm?

Doubt in proof of Jordan - von Neumann theorem

The correct way to map a column vector into a row vector.

What surface is represented by $\mathbf{r}\cdot\mathbf{a} = \mathrm{const.}$?

How to get a vector from two points

Bound on $|x \cdot y|$ from below

Proof that an operator is self-adjoint if and only if its matrix is self-adjoint

For a compact group $G$ and any finite-dimensional complex representation $(\pi,V)$, how to show that $V$ admits an invariant inner product?

Comparison of the expectation of minimums of random variables

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