So now we know some of the basic matrix algebraic operations and the concept that we started last was
transpose of the Matrix.
So over here, let's say for Matrix is denoted is a then transpose of the matrix is denoted as a dash.
There is even a concept called identity crisis, identity matrix is the one in which all the diagonal
elements are one and arrest all are zero.
So if you see these three matrices, one is a two by two matrix.
Another is a three by three matrix.
And the third one is a four by four matrix.
In all these three matrix, you will see that the diagonal elements are one and risk all elements are
zero.
There is a concept called convertible mattresses, inaudible mattresses are basically where you multiply
it with B and you get an identity matrix or B with A, you get identity matrix in these cases is equal
to be inverse or B is equal to a inverse.
Let's take a very simple example so that we understand how.
B is called inversed or is called B inverse.
You see over here have taken two mattresses, is equal to two, three, one, two, and B is equal to
two minus three, minus one, two.
Now, let's see if we do the product of a bit B.
In these cases, when we do, if it be or be it, you get an identity matrix like this, in this situation
we call B is equal to inverse or equal to be inverse of very simple example of inaudible madrases.
Now, there is a very important phenomenon in quantum mechanics, which would require the concept of
a joint of the Matrix.
A giant of a matrix is denoted by a dagger, so the symbol that you see is called Dagger.
So a giant of the matrix is called a dagger.
What is it and how basically do you calculate it joined now, folks, we know what exactly is the transpose
of a matrix in the earlier section of complex numbers?
We studied a concept called a complex conjugate.
So now let's see if any other matrices, if in your matrix you have elements which are complex numbers
in those cases when you do.
The complex conjugate of this particular matrix and then to the transpose of it.
That's called a joint of the matrix, let's see for this particular example, how the ajoint of the
matrix is calculated.
So now what we do is first we'll take the complex conjugate of this particular matrix.
And the complex conjugate is nothing, but you just inverse the sign of imaginary part.
Very simple.
Step number two is to do the transpose of complex conjugate.
Yeah, so now we know what exactly is the complex conjugate of the Matrix.
Let's do the transpose of it.
And in transpose the rows and columns interchange.
So now two minus three, minus four, plus five seven.
Is that a giant of the matrix?
Fantastic.
This is called.
A dagger.
No, there is even a concept that we need to know in quantum mechanics that's called her Matrix.
If Matrix E is equal to a joint officer, we saw that a joint concert earlier.
Then it is a Tumnus, her mission matrix that is if is equal to a dagger, then it is called US Commission
Matrix.
Let's take an example.
Now.
Let's see, this is The Matrix.
If you do the ajoint of this matrix, so let's say if you do the complex conjugate of it and then to
the transpose of it, you will get the same matrix.
That's why this matrix is done, that's a commission matrix.
Now.
Let's see if Elnaggar is equal to a dagger, is equal to an identity matrix, then it is Dharmadasa
unitary matrix.
All right, so these were the concepts required in madrases guys for studying quantum mechanics, it
would be even useful when we studied Quantum Gate in the next series.
I hope the concepts of matrices are clear.
Cherche.