Raising a square matrix to a power, like squaring a number, involves multiplying it by itself a number of times. As an example how it works with a 2x2 matrix:
Imagine a 2x2 matrix called A:
A = [A B]
[C D]
To find A² (the square of A), multiply A by itself:
A² = A × A
Let's look at a specific example with numbers:
If A = [1 2]
[3 4]
Then A² is calculated as:
(1⋅1+2⋅3)(1⋅2+2⋅4)(3⋅1+4⋅3)(3⋅2+4⋅4)
Doing matrix multiplication:
A² = [7 10]
[15 22]
Therefore, the square of matrix A in this example is:
A² = [7 10]
[15 22]
The same process extends to higher powers of a matrix such as A³ (A cubed), by multiplying A three times.
Comments
Post a Comment