Newbetuts

If ${\bf v},{\bf w}\in\mathbb R^n$, $\lVert{\bf v}+{\bf w}\rVert=\lVert{\bf v}\rVert+\lVert{\bf w}\rVert$, what can you say about $\bf v$ and $\bf w$?

$||x|| \le ||x+ry||$ for all $r \ge 0 \implies \langle j(x), y \rangle \ge 0$, where $j$ is the duality map.

Is the unit sphere in a preHilbert space a total set?

Are these sequences total sequences?

Orthogonality of characters for powers of a character

A characterization of 'orthogonal' matrices

Are there two different ways to generalize the orthogonal group?

Maximizing weighted sum of eigenvalues of a matrix ($\Lambda_1 U^\top \Lambda_2 U \Lambda_1$)

Why, if a matrix $Q$ is orthogonal, then $Q^T Q = I$?

Show that vector v is equal to the zero vector

Given $|| u + v || = || u - v ||$ show $\langle u , v\rangle = 0$

Loomis and Sternberg - Orthogonality and Scalar Product

How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)

If $\dim(A) \lt \dim(B)$, show that there is a non-null vector of $B$ orthogonal to every vector of $A$

If $M$ is a closed subspace of an Hilbert space $H$, then $M^{\perp\perp}=M$

Find the maximum of $\operatorname{Tr}(RZ)$ over all orthogonal matrices $R$

Finding Orthogonal Basis For $W^{\perp}$

New posts in orthogonality

Range of A and null space of the transpose of A

Legendre Polynomial Orthogonality Integral

If $M=M^{\perp\perp}$ for every closed subspace $M$ of a pre-Hilbert space then $H$ is complete

If ${\bf v},{\bf w}\in\mathbb R^n$, $\lVert{\bf v}+{\bf w}\rVert=\lVert{\bf v}\rVert+\lVert{\bf w}\rVert$, what can you say about $\bf v$ and $\bf w$?

$||x|| \le ||x+ry||$ for all $r \ge 0 \implies \langle j(x), y \rangle \ge 0$, where $j$ is the duality map.

Is the unit sphere in a preHilbert space a total set?

Are these sequences total sequences?

Orthogonality of characters for powers of a character

A characterization of 'orthogonal' matrices

Are there two different ways to generalize the orthogonal group?

Maximizing weighted sum of eigenvalues of a matrix ($\Lambda_1 U^\top \Lambda_2 U \Lambda_1$)

Why, if a matrix $Q$ is orthogonal, then $Q^T Q = I$?

Show that vector v is equal to the zero vector

Given $|| u + v || = || u - v ||$ show $\langle u , v\rangle = 0$

Loomis and Sternberg - Orthogonality and Scalar Product

How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)

If $\dim(A) \lt \dim(B)$, show that there is a non-null vector of $B$ orthogonal to every vector of $A$

If $M$ is a closed subspace of an Hilbert space $H$, then $M^{\perp\perp}=M$

Find the maximum of $\operatorname{Tr}(RZ)$ over all orthogonal matrices $R$

Finding Orthogonal Basis For $W^{\perp}$