# A term to explain a matrix that is mirror reflection of the input

What is the correct word to say that we have put everything that is in the right to the left and every thing that is placed in right to the left, while preserving the order in the opposite manner. What is the correct and appropriate word for it? I know that if it was just about a string of characters I could use reversed output. But now I have two dimensional objects (i.e. matrices). They topside and downside don't change but the right and left side are exchanged peer to peer.

``````1  2  3  4  5  6               6  5  4  3  2  1

7  8  9  10 11 12     ---->    12 11 10  9  8  7

13 14 15 16 17 18              18 17 16 15 14 13

``````

By searching on the internet I found the words and phrases: Reversed output, mirror output, mirror reflection of the input, reversed output, mirror reversed output. (One more question in parenthesis: Do we have the phrase "mirrorly reflected output"? Are we able to add -ly to mirror to use it as an adverb at all?)

And about its part of speech, I want to use it as an object, not a verb.

• I haven't seen it used for arrays, but "palindromic output" would probably be generally understood. Welcome, and please take the tour.
– Davo
Commented Sep 16, 2020 at 20:23
• This seems to be a duplicate of english.stackexchange.com/q/546834/216106
– Davo
Commented Sep 16, 2020 at 20:26
• @ Davo: Thanks. but palindromic means that it has the same meaning if it is either read from left or from the right, yes? But my matrix is not like that. I have just exchanged every thing in a position from the origin, with something with equal distance to the end.
– m123
Commented Sep 16, 2020 at 20:28
• @ Davo : Thanks but I asked for a general term there. Since I thought may be a special word for matrices or mathematics exist.
– m123
Commented Sep 16, 2020 at 20:31
• @ Dhanishtha Ghosh : Thanks. Inverted matrix has a technical meaning in mathematics. It means a matrix that if you multiply it to the original matrix, you will receive identity matrix. But this matrix is not that.
– m123
Commented Sep 16, 2020 at 20:35

Matlab has an operation for that:

B = fliplr(A) returns A with its columns flipped in the left-right direction (that is, about a vertical axis). If A is a row vector, then fliplr(A) returns a vector of the same length with the order of its elements reversed. If A is a column vector, then fliplr(A) simply returns A. For multidimensional arrays, fliplr operates on the planes formed by the first and second dimensions.

Taking a cue from that, you might define what you are talking about as you have above, and refer to it as "a flipped matrix/array", or as "an array flipped left-to-right". Subsequently, you can refer to it as "the flipped matrix/array". Then people will understand just what you mean.

The two dimensional figure on the right is the mirror image of the figure on the left (and vice versa). In technical terms, something's mirror image is its reflection over a line. In your figure, the line is the vertical line through the center of the figure. Points to the left of the line are reflected to corresponding points to the right, and vice versa.

Courtesy of Commons, this photo shows a fire truck painted with the word "FIRE" and its mirror image (so that one or the other will be readable whether viewed directly or through a car's mirror):

In mathematics, I'm not aware of a specific name for a 2D matrix which has this property. There is something called a centrosymmetric matrix but this requires symmetry about the center, not just in one axis (and the matrix must therefore be square). If your question is really mathematical in nature, you might get a better answer on Mathematics Stack Exchange.

• But the answer still won't be mirror matrix. Because that is a total different concept in Mathematics. Commented Sep 16, 2020 at 20:45
• @DhanishthaGhosh As I note in the answer, I'm not aware of a mathematical term for such a matrix. (I have an undergraduate degree in mathematics. There may be a term I'm not aware of, but I doubt it. This property isn't too common or useful in most matrices.) "Mirror matrix" is also not a thing. Commented Sep 16, 2020 at 20:46
• True. I meant no disrespect when I commented on your answer. But it is true that these type of matrices are rare. Though I must say, I just found an article about mirror matrix about the diagonal. Might be it is because there is a explicit mentioning of "about diagonal". geeksforgeeks.org/mirror-matrix-across-diagonal. Do you mind helping me with this? Commented Sep 16, 2020 at 20:51
• @TypeIA: This is not an inherent property of a matrix. I actually want to say transform matrix A to matrix B, in a way that matrix B elements are mirror refection (or something like that) of matrix A. So, I don't think it is a mathematical question or it has a technical word in mathematics. But the reason I mentioned that I exactly want it for matrices is that I searched for some words that are used for images, but when I use it along with matrices It seems odd to me. So, I am searching for a word that is suitable for matrices, but it may not limited to matrices or technical.
– m123
Commented Sep 16, 2020 at 21:14
• @TypeIA:... it may not be limited to matrices or be technical. Even or it may be limited or technical.
– m123
Commented Sep 16, 2020 at 21:22

For an image, we can say that it's reflected about the vertical axis. However, for a matrix, that's not quite appropriate. As just one example of the questions that might arise from that terminology, if one of the entries is 21, then are we changing that to 12? It's probably better to say "columns reversed". To make a noun version, you can say "The matrix with its columns reversed" or "column-reversed matrix".

To address the concern you raised in a comment, you could say "column order reversed".

• @ Thanks. "columns reversed" seems nice. But I guess it is a little vague. Since, when I am thinking about columns reversed, I feel that I should make each column upside down. Maybe it can get more accurate using an adjective which refers to the direction. But if this is the case, which adjective?
– m123
Commented Sep 16, 2020 at 21:00