4D Orthogonal Vector Space

[Anonymous No.15472026]

so anons...Im coding some stuff and I need to know if this is true
so...given a vector V1

if in 2D space vectors orthogonal to V1 ocupy a 1D space
and in 3D space vectors orthogonal to V1 ocupy a 2D space
then
it follows that in 4D for any given vector V1 there should be a 3D space of orthogonal vectors right?
IQ < 120 need not apply

[Anonymous No.15472034]

>>15472026
AI garbage

[Most Nicest No.15472038]

>>15472034
ok boomer

[Anonymous No.15472044]

>>15472026
Yes, trivially.

[Anonymous No.15472052]

>AI generated lust provoking image
>irrelevant, time-wasting question

[Anonymous No.15472058]

>>15472026
Yes, that statement is correct. In general, in n-dimensional space, the orthogonal complement of a vector V1 forms an (n-1)-dimensional subspace.

To understand this concept, let's consider some examples:

2D Space: In 2-dimensional space, a vector V1 defines a line. The vectors orthogonal to V1 (perpendicular to V1) will form a 1-dimensional space, which is the line perpendicular to V1.

3D Space: In 3-dimensional space, a vector V1 defines a plane. The vectors orthogonal to V1 will form a 2-dimensional space, which is the plane perpendicular to V1.

4D Space: Extending this pattern, in 4-dimensional space, a vector V1 will define a 3-dimensional subspace. The vectors orthogonal to V1 will form a 3-dimensional space, which is the subspace perpendicular to V1.

So, for any given vector V1 in 4D space, there will indeed be a 3D space of orthogonal vectors. This pattern continues for higher-dimensional spaces as well.

[Anonymous No.15472085]

>>15472026
>>15472058
OP, this anon answers you well, you'd do well to listen to him.
However given that no one is around to play the part of the strict mathematician, I suppose I will even though I'm not one.
There's a trivial exception, the zero vector which will be orthogonal to everything else.
Best of luck OP

[Anonymous No.15472117]

>>15472026
People can't possibly find giga tits like that attractive, can they? They look so grotesque to me.

[Most Nicest No.15472152]

>>15472058
thank you most based of sirs

[Most Nicest No.15472156]

>>15472117
I just post this shit img so that my post stands out from the rest

[Most Nicest No.15472158]

>>15472058
so assuming that I have an eigan vector of a symetrical 4x4 matrix that implies that the second eigan vector or eigan space will ocupy a 3D subspace ? correct
therefore to compute one of the eigan vectors in this subscpace one coud just atribute random values to X Y Z and calculate N so that the dot product of the two eigan vectors = 0
this way I have a second eigan vector

[Most Nicest No.15472161]

>>15472052
IQ < 120
go waste time talking about muh IQ and is X european bullshit

[Anonymous No.15472405]

>>15472026
>IQ < 120 need not apply
>asks high school math question

[Anonymous No.15472417]

>>15472158
>eigan vector

[Anonymous No.15472462]

>>15472026
Oh GOD I love big titted witches

[Anonymous No.15472475]

[Anonymous No.15472584]

>>15472026
this is true, this seems intuitive and i can prove it using the course we had only three weeks earlier on pre-hilbertian spaces ‑ including euclidian spaces in finite dimensions -
the space vecors orthogonal to V1 is called an hyperplan in linear algebra and for a vector space of n dimensions the dimension of an hyperspace is always n-1

[Anonymous No.15472610]

>>15472475
lol that' pic is of an effort by AI to troll stupid humans. AI has sense of humour.

[Most Nicest No.15473174]

>>15472417
yup not a native speaker my spelling is lacking

[Anonymous No.15474937]

>>15472026
prompts and model? upload original picture to catbox if you don't know