What does the superscripted notation in matrix notation mean?

[mcgruff]

This should be a really easy question, but I can't easily find the answer in any of my books. Anyway, in an old test question, the notation...

M¹⁰⁰

...is used. The question gives M as a 3x3 matrix as follows

0 1 0
0 0 1
1 0 0

...and then it asks for M¹⁰⁰.

From the key, I know the answer is still...

0 1 0
0 0 1
1 0 0

...however, I'm not sure what the superscripted notation means. Could someone please fill me in? Thanks.

 

[joeblow]

Multiply M by itself 100 times. What you have is an product of elementary matrices, so it has finite order. That should simplify calculations.

 

[mcgruff]

Multiply M by itself 100 times. What you have is an product of elementary matrices, so it has finite order. That should simplify calculations.

Thanks for the explanation. That makes sense. I feel sort of dumb---I thought it was some notation I hadn't seen before, given that is was three digits for a 3x3 matrix, not simply an exponent.

 

[HallsofIvy]

Actually, you only need to calculate $A^3$. From that you should be able to see what all powers of A are.

 

[blue_raver22]

The superscripted notation in this context refers to the power or exponent of the matrix. In this case, M100 means to multiply the given matrix M by itself 100 times. This is also known as matrix exponentiation. The resulting matrix will still be the same as the original matrix, as shown in the given answer. This notation is commonly used in linear algebra and has various applications in fields such as physics, engineering, and computer science. I suggest looking into further resources on matrix exponentiation to gain a better understanding of its significance and applications.