Question

Let $w$ be a positive continuous function for which $\int_0^1 w(x)dx = \int_0^1 x^2w(x)dx = 1$. Prove that $\int_0^1 xw(x)dx < 1$.

score 59 · Answer 1 · 2026-03-26 17:50:21

59

Views

Let $w$ be a positive continuous function for which $\int_0^1 w(x)dx = \int_0^1 x^2w(x)dx = 1$. Prove that $\int_0^1 xw(x)dx < 1$.

Published on 26 Mar 2026 - 17:50

score 152 · Answer 2 · 2026-04-14 10:49:32

152

Views

Prove/Disprove an inner product on a complex linear space restricted to its real structure is also an inner product

Published on 14 Apr 2026 - 10:49

score 171 · Answer 3 · 2026-04-15 18:45:41

171

Views

Physical meaning of the dot product of a vector and its laplacian

Published on 15 Apr 2026 - 18:45

score 317 · Answer 4 · 2026-04-16 12:59:37

317

Views

If every two-dimensional (vector) subspace of a normed space is an inner product space, then so is that normed space

Published on 16 Apr 2026 - 12:59

score 52 · Answer 5 · 2026-04-16 11:36:12

52

Views

Equality of inner product of outerproducts of vector with itself d-times and the d-th power of the inner product of the two vectors

Published on 16 Apr 2026 - 11:36

score 88 · Answer 6 · 2026-04-14 01:29:38

88

Views

Is the set of all random $n$-vectors with arbitrary expectations an inner product space?

Published on 14 Apr 2026 - 1:29

score 105 · Answer 7 · 2026-04-16 09:10:08

105

Views

Is each vector $y \in \{x\}^{\bot}$ a $r$-fold cross product of $x$ and some $x_1,...,x_{r-1}$?

Published on 16 Apr 2026 - 9:10

score 184 · Answer 8 · 2026-04-11 00:18:12

184

Views

Questions about the reflection operator on an inner product space

Published on 11 Apr 2026 - 0:18

score 71 · Answer 9 · 2026-04-12 09:58:37

71

Views

inner product trouble

Published on 12 Apr 2026 - 9:58

score 600 · Answer 10 · 2026-04-15 09:42:36

600

Views

Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.

Published on 15 Apr 2026 - 9:42

score 1k · Answer 11 · 2026-04-15 17:18:04

1k

Views

Prove that vectors of a real inner product space are linearly independent.

Published on 15 Apr 2026 - 17:18

score 87 · Answer 12 · 2026-04-15 11:51:46

87

Views

Uniqueness of a complex inner product, given a positive definite quadratic real-valued function

Published on 15 Apr 2026 - 11:51

score 31 · Answer 13 · 2026-04-09 14:09:21

31

Views

Checking for diagonalization.

Published on 09 Apr 2026 - 14:09

score 73 · Answer 14 · 2026-04-12 16:22:15

73

Views

Show there are arbitrary vectors and an orthonormal set in $V$, s. t. $A\in\mathcal L(V)$ can be defined in the given way.

Published on 12 Apr 2026 - 16:22

score 118 · Answer 15 · 2026-04-15 17:26:02

118

Views

Generality of the inner product

Published on 15 Apr 2026 - 17:26

List Question

Let $w$ be a positive continuous function for which $\int_0^1 w(x)dx = \int_0^1 x^2w(x)dx = 1$. Prove that $\int_0^1 xw(x)dx < 1$.

Prove/Disprove an inner product on a complex linear space restricted to its real structure is also an inner product

Physical meaning of the dot product of a vector and its laplacian

If every two-dimensional (vector) subspace of a normed space is an inner product space, then so is that normed space

Equality of inner product of outerproducts of vector with itself d-times and the d-th power of the inner product of the two vectors

Is the set of all random $n$-vectors with arbitrary expectations an inner product space?

Is each vector $y \in \{x\}^{\bot}$ a $r$-fold cross product of $x$ and some $x_1,...,x_{r-1}$?

Questions about the reflection operator on an inner product space

inner product trouble

Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.

Prove that vectors of a real inner product space are linearly independent.

Uniqueness of a complex inner product, given a positive definite quadratic real-valued function

Checking for diagonalization.

Show there are arbitrary vectors and an orthonormal set in $V$, s. t. $A\in\mathcal L(V)$ can be defined in the given way.

Generality of the inner product

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