Matrices, Row, Column, Matrix operations, Scalar multiplication, Addition, Multiplication, Commutative, Associative, Vectors, Vector operations, Scalar multiplication, Addition, Multiplication, Commutative, Associative, Dot product, Dyadic product.
Now we have a few matrices and vectors, and we need to do a few operations on them.
Well, let's do them one by one.
There is a little problem here. doesn’t work.
Unfortunately there is no trick for exponentiation of matrices, so if we need the square of this matrix, we have to raise it to the second power by multiplying the matrix by itself.
If we needed to raise this matrix to the fourth power, that would take a long time.
But we are lucky, as we only need its square.
We only have left. We just hit the jackpot with this one, as is a diagonal matrix.
Diagonal matrices are easy to raise to powers, because all we have to do is take the elements of the main diagonal one by one, and raise them to the required power.
This method only works for diagonal matrices, but it does wonders there.
If we multiplied it for times in a sequence, we would get the same result,
except slower – if you want to verify this, try it yourself and see.