How do you call a^(- 1) in relation to a nonzero number a?
inverse
We want to complete the given sentence.
If there exists an n* n matrix A^(- 1) such that A^(- 1)A=I_n = AA^(- 1), then A^(- 1) is called the of A.
Here, I_n represents the n* n identity matrix.
[
ccccc
1 & 0& 0 & ... & 0
0 & 1 & 0 & ... &0
... & &⋱ & & ...
0 & ... & 0 &1 & 0
0 &... & 0 &0 & 1
]
Let's imagine a similar statement in real numbers.
a^(- 1)a = 1 ⇒ a^(- 1)=1/a
If a≠0, then a^(- 1) is called the inverse of number a. We will say the same for matrices, matrix A^(- 1) is called the inverse of matrix A. Let's fill in the blank!
If there exists an n* n matrix A^(- 1) such that A^(- 1)A=I_n = AA^(- 1), then A^(- 1) is called the inverse of A.
