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I'm a student of mathematics in Germany.


Mar
10
revised Prove that $\frac{x^2+1}{x^2(1-x)}>8$ for $x\in(0,1)$
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Mar
10
answered Prove that $\frac{x^2+1}{x^2(1-x)}>8$ for $x\in(0,1)$
Mar
10
comment Prove that $\frac{x^2+1}{x^2(1-x)}>8$ for $x\in(0,1)$
$x^2(1-x) > 0$ for $x ∈ (0..1)$, so instead show $x^2+1 > 8x^2(1-x) = 8x^2 - 8x^3$.
Mar
10
revised $M \rightarrow M^T M$ is a continuous mapping.
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Mar
10
answered $M \rightarrow M^T M$ is a continuous mapping.
Mar
10
comment Let $A \in \operatorname{Mat}_n(\mathbb R), A(i,j) := \langle v_i,v_j\rangle$ where $v_1,\dotsc,v_n$ is a basis. Show $A$ is invertible.
@NicolasLykkeIversen Oh, yeah. You can.
Mar
10
answered Let $A \in \operatorname{Mat}_n(\mathbb R), A(i,j) := \langle v_i,v_j\rangle$ where $v_1,\dotsc,v_n$ is a basis. Show $A$ is invertible.
Mar
10
comment Let $A \in \operatorname{Mat}_n(\mathbb R), A(i,j) := \langle v_i,v_j\rangle$ where $v_1,\dotsc,v_n$ is a basis. Show $A$ is invertible.
Maybe this is yet to prove!
Mar
10
comment Let $A \in \operatorname{Mat}_n(\mathbb R), A(i,j) := \langle v_i,v_j\rangle$ where $v_1,\dotsc,v_n$ is a basis. Show $A$ is invertible.
I think $[y]_U$ should denote the coordinates of $y$ in base $U$. This identity holds for abstract inner product spaces as well.
Mar
10
comment Let $A \in \operatorname{Mat}_n(\mathbb R), A(i,j) := \langle v_i,v_j\rangle$ where $v_1,\dotsc,v_n$ is a basis. Show $A$ is invertible.
Depends on whether $V = ℝ^n$ and “〈–,–〉” denotes the euclidean inner product.
Mar
10
comment Let $A \in \operatorname{Mat}_n(\mathbb R), A(i,j) := \langle v_i,v_j\rangle$ where $v_1,\dotsc,v_n$ is a basis. Show $A$ is invertible.
Depends on whether $V = ℝ^n$ and “$〈–,–〉$” denotes the euclidean inner product.
Mar
10
comment Let $A \in \operatorname{Mat}_n(\mathbb R), A(i,j) := \langle v_i,v_j\rangle$ where $v_1,\dotsc,v_n$ is a basis. Show $A$ is invertible.
Do you know that you can orthogonalize bases in finite dimensional real inner product spaces?
Mar
10
comment Category Theory: Why arrows?
Have you had a look at allegories? I mean, not that binary relations wouldn’t define arrows as well. Binary relations are directed.
Mar
10
answered $B$ is similar to $C$ if and only if $A\oplus B$ is similar to $A\oplus C$
Mar
9
answered Prove that $gcd(a, b) = gcd(a, b + ma)$?
Mar
9
comment Prove that $gcd(a, b) = gcd(a, b + ma)$?
$\mathrm{mcd}$ being the most great common divisor?
Mar
9
revised A function vanishing at infinity is uniformly continuous
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Mar
9
revised A function vanishing at infinity is uniformly continuous
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Mar
9
comment A function vanishing at infinity is uniformly continuous
@FrauenarztDoktorFotzenglotz Okay, thanks. Anyway, then I interpreted it correctly and it should work out. Merely the first paragraph is superfluous.
Mar
9
comment A function vanishing at infinity is uniformly continuous
@FrauenarztDoktorFotzenglotz No, if it is different from $C^0(ℝ)$. How is it defined?