Identity Matrix
First, some definitions!
A Matrix is an array of numbers:
764 142−2 309
A Matrix
(This one has 3 Rows and 3 Columns)
(This one has 3 Rows and 3 Columns)
We talk about one matrix, or several matrices.
The Main Diagonal starts at the top left and goes down right:
Identity Matrix
An Identity Matrix has 1s on the main diagonal and 0s everywhere else:
I =
100 010 001
A 3×3 Identity Matrix
- It is square (same number of rows as columns)
- It can be large or small (2×2, 100×100, ... whatever)
- Its symbol is the capital letter I
It is the matrix equivalent of the number "1". Multiplying it with another matrix leaves the original unchanged:
A × I = A
I × A = A
Some More Identity Matrices
I2 =
10 01
A 2×2 Identity Matrix
I4 =
1000 0100 0010 0001
A 4×4 Identity Matrix
In =
10...0 01...0 00...0 00...1
A General Identity Matrix