Examples of using Lambda is equal in English and their translations into Polish
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This corresponds to lambda is equal to minus 3.
When lambda is equal to minus 1,
Because it corresponds to lambda is equal to minus 3.
Let's say for lambda is equal to 5, the eigenspace that corresponds to 5 is equal to the null space of?
And we got our eigenvalues where lambda is equal to 3 and.
So if lambda is equal to minus 3-- I will do it up here, I think I have enough space-- lambda is equal to minus 3.
So this is the eigenspace for lambda is equal to 3.
The eigenspace for lambda is equal to 3, is equal to the span, all of the potential linear combinations of this guy
Let's do the one that corresponds to lambda is equal to minus 3.
So, the eigenspace that corresponds to lambda is equal to minus 3, is the null space,
So what this tells us, this is the eigenspace for lambda is equal to minus 3.
So if lambda is equal to 3, this matrix becomes lambda plus 1 is 4,
And then the eigenspace for lambda is equal to minus 3 is a line.
our 3 by 3 matrix A that we had way up there-- this matrix A right there-- the possible eigenvalues are: lambda is equal to 3 or lambda is equal to minus 3.
We can say that the eigenspace for lambda is equal to 3,
And then that times vectors in the eigenspace that corresponds to lambda is equal to minus 3, is going to be equal to 0.
Or another way to say it is that the eigenspace for lambda is equal to minus 3 is equal to the span-- I wrote this really messy-- where lambda is equal to minus 3 is equal to the span of the vector minus 2, 1, and 1.
if you have some vector in this eigenspace that corresponds to lambda is equal to 3, and you apply the transformation.
So the eigenspace for lambda is equal to minus 1 is going to be the null space of lambda times our identity matrix,
our characteristic polynomial, are lambda is equal to 5 or lambda is equal to minus 1.
A times v is equal to lambda v.
We said that if you were trying to solve A times some eigenvector is equal to lambda times that eigenvector, the two lambdas, which this equation can be solved for, are the lambdas 5 and minus 1.
only if the 0 vector is equal to lambda times the identity matrix minus A times v.
If this transformation matrix can be represented as a matrix vector product-- and it should be; it's a linear transformation-- then any v that satisfies the transformation of-- I will say transformation of v is equal to lambda v, which also would be-- you know, the transformation of[? v?] would just be A times v.