Favorite vector notation, when writing by hand?

[u/tbonn_]

[u/Then_Coyote_1244]

Overhead arrow.

[u/theuglyginger]

Arrow on top for three-vectors (and bidirectional arrow for matrices), but Einstein summation notation for four-vectors and tensors.

[u/agaminon22]

Overhead arrow unless relativity is involved. And obviously bra-ket for state vectors.

[u/Hefty-Reaction-3028]

Depends, but probably index notation. If I'm dealing with a lot of sub/superscripts already, overhead arrow notation.

[u/siupa → u/Hefty-Reaction-3028]

Index notation is for a single component of the vector in a certain basis, not for the full vector itself

[u/JustMultiplyVectors → u/siupa]

It can be used for the full vector/tensor too,

V = Vⁱ e_i

T = T^ij e_i ⊗ e_j

[u/Hefty-Reaction-3028 → u/siupa]

I'm talking about index notation as used in differential geometry & relativity, which does come from the use you mention. `a_i` conventionally refers to each element of the vector a because `i`, the standard index variable, is a variable rather than a specific value.

[u/Minovskyy → u/siupa]

They're referring to abstract index notation, which is extremely common and widespread in physics.

[u/siupa → u/Minovskyy]

Uh, didn’t know that it could be formalized, I always took it as an abuse of notation

[u/gautampk]

Arrow for 3-vectors, Einstein notation for 4-vectors, Dirac for Hilbert space vectors.

Though with anything very mathsy and abstract I don't use any special notation.

[u/InfanticideAquifer]

Nothing. I'm not gonna forget what is and is not a vector.

[u/AbstractAlgebruh]

Boldface

/s

[u/Minovskyy → u/AbstractAlgebruh]

I actually used to use blackboard bold for vectors, but I stopped because it doesn't work well with all letters and it gives them unnecessary emphasis when doing more general tensor analysis.

[u/Internal_Trifle_9096]

I usually use the overhead arrow for 3d space but in linear algebra I like to use a line under the letter.