What is positive and negative eigenspaces? Can you recommend me a

Thread starter seydunas
Start date Aug 12, 2011
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In summary, positive eigenspace is the subset of a vector space containing eigenvectors corresponding to positive eigenvalues, while negative eigenspace is the subset containing eigenvectors corresponding to negative eigenvalues. They are both related as part of the eigenspace and help us understand the behavior of linear transformations on a vector space. Recommended resources for learning more about this topic include the Khan Academy's Linear Algebra course and textbooks such as "Introduction to Linear Algebra" and "Linear Algebra and Its Applications."

Aug 12, 2011

seydunas

What is positive and negative eigenspaces? Can you recommend me a referance to know them?

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Aug 23, 2011

tiny-tim

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hi seydunas!

try http://dusanstos.angelfire.com/Dirac_equation.htm"

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Aug 23, 2011

quasar987

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Guess: the eigenspace associated with a positive (resp. negative) eigenvalue?

What is positive eigenspace?

Positive eigenspace refers to the subset of a vector space that contains all the eigenvectors corresponding to positive eigenvalues of a given linear transformation. In simpler terms, it is the set of all vectors that remain in the same direction after being multiplied by a matrix.

What is negative eigenspace?

Negative eigenspace is the opposite of positive eigenspace and refers to the subset of a vector space that contains all the eigenvectors corresponding to negative eigenvalues of a given linear transformation. It is the set of all vectors that change direction and point in the opposite direction after being multiplied by a matrix.

How are positive and negative eigenspaces related?

Positive and negative eigenspaces are related because they are both part of the eigenspace of a given linear transformation. They represent the different directions in which the vectors in a vector space are transformed when multiplied by a matrix.

What is the significance of positive and negative eigenspaces?

Positive and negative eigenspaces are important in linear algebra because they help us understand the behavior of a linear transformation on a vector space. They also help us identify the directions in which a transformation stretches or compresses the vectors in a space.

Can you recommend me a resource to learn more about positive and negative eigenspaces?

Yes, I would recommend checking out the Khan Academy's Linear Algebra course. They have a comprehensive section on eigenvectors and eigenvalues, including positive and negative eigenspaces. Additionally, textbooks such as "Introduction to Linear Algebra" by Gilbert Strang and "Linear Algebra and Its Applications" by David C. Lay are also great resources for learning more about this topic.