Examples of using Identity matrix in English and their translations into Polish
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This is the identity matrix in Rk.
I simplified it, butthis is almost the identity matrix.
The identity matrix times v is just v.
Well that's just the identity matrix.
The identity matrix is always going to be n-by-n.
Lambda times the identity matrix times A.
So I multiplied this by a inverse,to get to the identity matrix.
So that's the identity matrix times lambda.
I just subtracted Av from both sides,rewrote v as the identity matrix times v.
I put the identity matrix of the same size.
Something times C is the identity matrix.
Lambda times the identity matrix minus A ends up being this.
Well, what is 5 times the identity matrix?
That's the identity matrix, times x is equal to a inverse b.
I get the k by k identity matrix.
I get the identity matrix of k, because it's going to be k by n, times n by k.
This is lambda times the identity matrix in R3.
You take your identity matrix and you perform the transformation on each of its columns.
Which is really just a fancy way of saying,let's turn it into the identity matrix.
The identity matrix times any other matrix is just that matrix. .
Then if I take the composition of h with f,I have to get the identity matrix on the set X.
And we get lambda times the identity matrix minus A times my eigenvector have got to be equal to 0.
I'm essentially multiplying-- when you combine all of these-- a inverse times the identity matrix.
So if I take the determinate of lambda times the identity matrix minus A, it has got to be equal to 0.
But what we do know is by multiplying byall of these matrices, we essentially got the identity matrix.
So lambda times the identity matrix minus A is going to be equal to-- it's actually pretty straightforward to find.
We know lambda times some eigenvector is the same thing as lambda times the identity matrix times that eigenvector.
So it almost looks like the identity matrix, but we flipped our third vector, and that's why we got a minus 1 there.
Well this is only true if andonly if the 0 vector is equal to lambda times the identity matrix minus A times v.
The identity matrix had 1's across here, so that's the only thing that becomes non-zero when you multiply it by lambda.