What is the difference between n-dimensional unit column vector and n-dimensional unit vector

What is the difference between n-dimensional unit column vector and n-dimensional unit vector

The latter is that the vector has n components, the former represents n vectors (can have any component)

What is the n-dimensional unit coordinate vector group definition?

0

What is the necessary and sufficient condition for nonzero n-dimensional vectors a1, a2 to be linearly independent?

Components corresponding to a1, a2 are not proportional

A Necessary and Sufficient Condition of Linear Independence a1a2a3...am n-dimensional Vector Group b1b2.bm Matrix A =(a1a2...) is equivalent to why matrix B =(b1b2.)

The Rank Similarity of Matrix Equivalent Regular Matrix
So r (b1,..., bm)= r (B)= r (A)= r (a1,..., am)= m
So b1,...,bm linearly independent

The Rank Homogeneity of Matrix Equivalent Regular Matrix
So r (b1,..., bm)= r (B)= r (A)= r (a1,..., am)= m
So b1,...,bm linearly independent

Let a1, a2,..., an be a set of linearly independent n-dimensional vectors.

Let a be any n-dimensional vector.
Because a1, a2,..., an, a is n+1 n-dimensional vectors,
So a1, a2,..., an, a are linearly related.
And because a1, a2,..., an is linearly independent,
So r (a1, a2,..., an, a)= r (a1, a2,..., an)= n
Thus a can be expressed linearly by a 1, a 2,..., an, and the expression is unique.

What is "dimension" in n-dimensional vector? Is the dimension of an n-dimensional vector a row or a column or something else? Thank you very much for asking for an answer. What did the "dimension" in the N-dimensional vector mean! Is the "dimension" of the N-dimensional vector referring to "row" or "column" or something else? Asking for an answer from an expert is extremely grateful What does the "dimension" in the N-dimensional vector mean! Is the "dimension" of the n-dimensional vector referring to "row" or "column" or something else? Thank you very much for asking the expert for an answer

Refers to coordinates
For example, a one-dimensional vector is represented by only one number
Two-dimensional vectors are expressed in two numbers. Example n (1,1)
Similarly,3D is represented by three numbers. Example n (1,1,1)
Of course, both have arrows.