(putting an image of eigen because i love eigenvector very much)
Eigenvector loves to joke about things in the appropiate circumstances, ei also like to create lots of memes. Ei're very silly and consider genself a shitposter, ei are also considered one by others.
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Eigenvector not only goes by ei/gen/vec/tors, eigenvector also loves being referred without any pronouns, especially because ei love hearing vec name so much, therefore eigenvector goes by ei/none, ei being the eigenvector pronoun set. Eigenvector also loves nameself pronouns, similar to nullpronomiality, except with nameself pronouns having a -self form which is just, well, the name plus self. I love Eigenvector so much, and eigenvector loves eigenvectorself too. Vec nameself pronouns aren't exclusively eigenvector/eigenvectorself, but also eigen/eigenself. All praise the eigenvector.
Remember Eigenvector (ei/gen/vec/tors, formatted as they/them/their/theirs)?
I made a design for gen! (this sounds like if ei weren't mine. I made gen.)
Vec design has several references towards eigenvectors (of course).
Ei have an identity matrix, which is analogous to an eigenvector, because applying an identity matrix as a geometric transformation to something doesn't change it at all, much like how an eigenvector is unchanged by a transformation.
Vec design has lots of color patches that resemble hearts as a reference to Undertale souls, which resist during death due to having determination, much like how eigenvectors remain unchanged after a transformation. Ironically, though, the value of an eigenvector's determinant is zero, which sounds like having zero determination, "det = 0" is written on the right side (vec point of view) of vec face.
For example, if one draws lines across vec hair and ears, they form the second part of the equation of the eigenvector.
The arrows on vec huge hair tuft (?) is based on this image.
Vector and Eigenvector! (Element Cattos, more specifically, Math Cattos)
So uh, I have this catto named Integral Symbol, right? Well, I wanna show y'all my other math cattos!
Lots of text here, so it's under this. Yay!
Ve uses ve/it/they pronouns and its gender is "vector", without the quotes, not to be confused with the unrelated gender named "vectorgender", vir first pronoun set, "ve/vi" is also based on themself. Vir collar is a cartesian plane, since vectors are also located in it, also they have an arrow on top of its head, another nod to how vectors are sometimes represented with arrows. It believes that going around with a scooter makes them look "swag", also ve likes going around on their scooter really fast for fun. They love skateboards and scooters, due to them being used often in physics textbooks to demonstrate motion with vectors, however, sometimes ve's not careful and crash into people.
Vector
Eigenvector
Image goes here, I don't have an image of gen yet.
Ei uses ei/gen/vec/tors pronouns. Due to the nature of vec gender, vec gender deserves its own section here due to its length.
Vec distinct hairstyle is due to it resembling the notation of an eigenvector. Image below is from 3Blue1Brown.
Eigenvector's gender.
Vec gender is quite complex, but it's primarily described by "eigenvectorgender", which is a xenogender where one's gender is like an arrow that points in a direction and thus contains its own gender alignment, but isn't aligned to an existing gender, thus independent like an actual eigenvector. By logic, due to gen being an eigenvector, vec gender is also a nominalgender due to being unique to gen, but is also an auingender due to being autonomous in nature, and an eigengender due to not being influenced by anything. To put it short, vec gender is based on genself, *is* genself, isn't influenced by anything and is thus a literal eigenvector, too. In vec own words, "My gender is me, and only me". On the wiki, list vec gender as simply "eigenvector", without the quotes, instead of "eigenvectorgender" since, as ei said, "my gender is me". Vec pronouns are also clearly based on genself.
Personality and other things.
Ei have an extremely high self-esteem, however, ei're not selfish, ei're actually quite friendly, ei can act very blunt when bothered, though.
Vector and Eigenvector's kinship.
They are siblings due to being vectors, they also get along really well with eachother.
Ei like to joke about how apparently Vector's scooter is "derivable", a play on how acceleration is a derivative, and thus, to find the acceleration of a scooter, you have to derive it, ve are comfortable with these jokes and even find them funny. Eigenvector also likes to spin Vector's scooter when they're using it, solely for fun, Vector isn't bothered by this. They both love Undertale and Deltarune, they also love watching 3Blue1Brown due to the linear algebra series that he (Grant Sanderson) created for it, they are also cyan due to the fact that some of the pi creatures from that channel are cyan.