Post History
#3: Post edited
by
Peter Taylor
·
2021-11-02T14:48:51Z (about 3 years ago)
Remove tags which don't seem likely to fit many questions and create one which does
#2: Post edited
What does variable in sup represent for matrix?
- What does upper indices represent?
I had seen people were representing matrix 2 way.- 1. $$\sum_{j=1}^n a_{ij}$$
- It is representing a column matrix (vector actually) if we assume $i=1$.
- $$\begin{bmatrix}a_{11} & a_{12} & a_{13} & ......\end{bmatrix}$$
- 2. $$\sum_{j=1}^n a^{ij}$$
What it is representing? At first I thought it was row matrix (vector) since it is opposite of column matrix (vector). But when I was writing the question I couldn't generate a row matrix using the 2nd equation. I confuse more when I see $a_j^{i}$ sometimes there's two variable in sub and sup. $a_{ji}^{kl}$ I don't remember if one of them matches (I meant I am not sure if I write it wrong way).
- I saw that people were representing matrices in two ways.
- 1. $$\sum_{j=1}^n a_{ij}$$
- It is representing a column matrix (vector actually) if we assume $i=1$.
- $$\begin{bmatrix}a_{11} & a_{12} & a_{13} & ......\end{bmatrix}$$
- 2. $$\sum_{j=1}^n a^{ij}$$
- What is it representing? At first, I thought it was a row matrix (vector) since it is the opposite of a column matrix (vector). But when I was writing the question I couldn't generate a row matrix using the 2nd equation. I became more confused when I saw $a_j^{i}$, and sometimes there are two variables in sub and sup: $a_{ji}^{kl}$. I don't remember if either of them matches (I am not sure if I wrote it the wrong way).
- After searching a little bit I found that when we move components our vectors don't change. But, I can't get deeper into **covariant** and **contravariant**. I even saw some people use an equation like this: $^ia_j$.
- I was reading https://physics.stackexchange.com/q/541822/, and those answers don't explain the covariant and contravariant for a beginner (those explanations are for those who have some knowledge of the covariant and contravariant).
- I was watching [the video](https://www.youtube.com/watch?v=CliW7kSxxWU), what he said that is, if we take some basis vectors and then find a vector using those basis vectors than if we decrease length of those vectors than that's contravariant vectors (I think he meant to say changing those components). But the explanation is not much more good to me. He might be correct also but I don't have any idea. If he is assuming that changes of basis vectors is contravariant then is "the original" basis vectors covariant? So how do we deal with covariant and contravariant altogether $g^i_j$ sometimes $g_j^i$
#1: Initial revision
What does variable in sup represent for matrix?
I had seen people were representing matrix 2 way.
1. $$\sum_{j=1}^n a_{ij}$$
It is representing a column matrix (vector actually) if we assume $i=1$.
$$\begin{bmatrix}a_{11} & a_{12} & a_{13} & ......\end{bmatrix}$$
2. $$\sum_{j=1}^n a^{ij}$$
What it is representing? At first I thought it was row matrix (vector) since it is opposite of column matrix (vector). But when I was writing the question I couldn't generate a row matrix using the 2nd equation. I confuse more when I see $a_j^{i}$ sometimes there's two variable in sub and sup. $a_{ji}^{kl}$ I don't remember if one of them matches (I meant I am not sure if I write it wrong way).