List questions from quadratic-forms

Published on 06 Jan 2014 - 22:56

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Associated Bilinear Form to Q (Quadratic Form)

Published on 28 Mar 2026 - 20:54

140

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Identify a quadric

Published on 29 Mar 2026 - 14:54

8.2k

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Polar form of quadratic equations

Published on 08 Jan 2014 - 22:41

598

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Finding diagonal transformation matrix of a bilinear form

Published on 28 Mar 2026 - 20:58

5.1k

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Is it true that the whole space is the direct sum of a subspace and its orthogonal space?

Published on 23 Feb 2026 - 17:26

64

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Showing that the quadratic form $Q(x,y,z,t)=x^2+y^2+z^2-7\cdot t^2$ is anisotropic on $\Bbb Q^4$

Published on 13 Jan 2014 - 16:24

9.4k

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Find the signature of the quadratic form

Published on 15 Jan 2014 - 12:04

294

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Signature of quadratic form $Q(p)=p(1)p(2)+p(3)p(4)$

Published on 15 Jan 2014 - 16:17

2.6k

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Find the symmetric matrix that represents the quadratic form $Q(X)=trace(X^2)$, $X\in mat_n\mathbb (R)$

Published on 15 Jan 2014 - 16:51

665

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Let $W \subset V$ vector spaces, let $W'$ be the orthogonal complement of $W$. Show $\dim(W)+\dim(W')=\dim V$

Published on 15 Jan 2014 - 18:33

648

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Congruent diagonal matrix

Published on 28 Mar 2026 - 22:24

1.2k

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Counting the Number of Integral Solutions to $x^2+dy^2 = n$

Published on 28 Feb 2026 - 1:15

597

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Is this expression a quadratic form

Published on 25 Jan 2014 - 15:47

158

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If $3\mid a,b,c$ and $n=a^2+b^2+c^2$, prove that there exist $x,y,z$ such that $n=x^2+y^2+z^2$, where $3\nmid x,y,z$.

Published on 29 Mar 2026 - 7:28

List Question

Quadratic formula / stationary points

Associated Bilinear Form to Q (Quadratic Form)

Identify a quadric

Polar form of quadratic equations

Finding diagonal transformation matrix of a bilinear form

Is it true that the whole space is the direct sum of a subspace and its orthogonal space?

Showing that the quadratic form $Q(x,y,z,t)=x^2+y^2+z^2-7\cdot t^2$ is anisotropic on $\Bbb Q^4$

Find the signature of the quadratic form

Signature of quadratic form $Q(p)=p(1)p(2)+p(3)p(4)$

Find the symmetric matrix that represents the quadratic form $Q(X)=trace(X^2)$, $X\in mat_n\mathbb (R)$

Let $W \subset V$ vector spaces, let $W'$ be the orthogonal complement of $W$. Show $\dim(W)+\dim(W')=\dim V$

Congruent diagonal matrix

Counting the Number of Integral Solutions to $x^2+dy^2 = n$

Is this expression a quadratic form

If $3\mid a,b,c$ and $n=a^2+b^2+c^2$, prove that there exist $x,y,z$ such that $n=x^2+y^2+z^2$, where $3\nmid x,y,z$.

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