Question

Is a matrix a vector? (i.e. a element of a vector space.)

Answer 1

I see them following all axioms of vector spaces, so I assume they would be?

Answer 2

the operations of addition and multiplication I am assuming are the commonly defined ones...

Answer 3

all vectors can be written as matrixes but not all matrixes are vectors

Answer 4

Well, they are both associative and commutative under addition, with existence of identity and inverse matrices...
furthermore scalar multiplication is compatible with field multiplication, and there exists an identity element of scalar multiplcation...

Answer 5

scalar multiplication is also distributive under both field and vector addition.

Answer 6

so, wouldn't every matrix be considered a vector as part of the definition of vector spaces?

Answer 7

vectors can be written as a matrix with either 1 row and n columns or n rows and 1 column
but matrixes can be many columns and rows
sorry about my crappy wording its 4 am 8D

Answer 8

@Phaen , I mean matrices being vectors with a vector being defined as an element of a vector space - I guess my question is: Are matrices elements of vector spaces under the normal definitions of addition and matrix multiplication?

Answer 9

Sorry, its been too many years since linear algebra class, I'm fuzzy on how to answer that D:

Goodnight inkyvoyd and have a wonderful day to you :)

Answer 10

Goodnight I guess...

Answer 11

matrix is a representation of data,it can be used to represent a vector too, or so i guess

Answer 12

the operations ei, lets see ahh nope you can just use them to indicate the matrix the matrixial operations don't apply to the,incase if you have to apply you gotta make the other matrix coloumn only and the first being row only

Answer 13

^ the coloumn and row in case of multiplication and finding the dot product, the addition will require considering them both in row only or coloumn only format, and cross product mhmm nope can't do the cross product