How can we turn a matrix to 180 degree in excel?

[soleimani1967]

We can easily turn a matrix to 90 degree by using of TRANSPOSE’ formula in excel. I am not a specialist in excel maybe there is another formula to turn a matrix to 180 degree. I utilized from below rule in set theory to solve this case as follows:
Let consider set “A” and power set of A which is set “C” as follows:
A = {a1, a2, a3, a4… an}
C = {{}, {a1}, {a2}, {a3}, {a4}, {a1, a2}, {a1, a3},….{an}}
Rule: Number of sets in power set (C) which are included sequence of numbers and for each specific size of members (r) can be calculated by below formula:
N (n, r) = n - r +1
Where: n = number of members set A, r = specific size of members in sets with sequence numbers
Example:
Assume, we have:
A = {1, 2, 3, 4} then
C = {{}, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}
n = 4,
r = 1, N (4, 1) = 4 and sets are: {1}, {2}, {3}, {4}
r = 2, N (4, 2) = 3 and sets are: {1, 2}, {2, 3}, {3, 4}
r = 3, N (4, 3) = 2 and sets are: {1, 2, 3}, {2, 3, 4}
r = 4, N (4, 4) = 1 and set is: {1, 2, 3, 4}
Case: How can we turn a matrix to 180 degree in excel?
Here, I am willing to show you my solution to solve this case step by step by an example and also using of above formula (N (n, r) = n - r +1 ) as follows:
- Assume we have a matrix of 16*8 including members of a, b, c…
- Copy matrix between cells N1:U1 and N16:U16
- On cell M1 to M16 fill numbers 1 to 16
- On cell A1 fill formula = 16 – M1 + 1 which is the same N (n, r) = n - r +1 and copy to A16
- On cell B1 copy below formula and copy to K1 and B16 to K16
=IFERROR(INDEX($M:$W,MATCH($A1,$M:$M,0),COLUMN(B1)),"")

Have you another solution to solve this case?

[Kaper]

Are you sure, it's 180 deg turn? I'd rather say it is mirrored against horizontal axis (or in other words, turned upside down).

[Kaper]

PS. to have N1:U16 really turned 180 degrees write somewhere (may be in B1 as your original solution)

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and copy right and down. (columns A and M formulas are not needed to have it working)

Note that TRANSPOSE is no really rotating 90 degrees, it is also mirroring but against diagonal (-45 deg).

[soleimani1967]

Sorry. Your formula does not work. It gaves a error on excel.

[Kaper]

Change semicolons to commas in the formula.

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[soleimani1967]

Thank you very much for your solution of a new one. It as well as works. You are true because when we speak about turning, we should specify the axis of turning. Unfortunately, I forgot to specify axis of turning. Now, I have two questions:
1. Could you please also specify the axis of turing for 180 degree in accordance with your formula? (It means that each member of matrix turns in related to a axis 180 degree)
2. Have you another formula or solution when the axis of turning is horizental (As you told: it is mirrored against horizontal axis (or in other words, turned upside down))?

[soleimani1967]

I have attached my example on excel file.Matrix_180.xlsx

[Kaper]

for such mirroring:

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would be enough

[Kaper]

Hava a look also on the picture. Leftmost transformation is transpose - mirroring vs tilted axis. In center is what you asked for - mirrored against horizontal mirror. Righmost what I understand as 180 degrees rotation.