What is linear algebra?
Q: What is linear algebra?
A: Linear algebra is a branch of mathematics that deals with the study of vector spaces and linear transformation.
Q: What is an eigenvector?
A: An eigenvector is a vector that does not change direction after undergoing a transformation, except in the case when the transformation turns it to the opposite direction.
Q: What does the term "null vector" mean?
A: A null vector is a vector of zero length or magnitude.
Q: What is an eigenvalue?
A: An eigenvalue is the value of the change in length of an eigenvector after undergoing a transformation.
Q: What is the significance of the eigenvalue in linear algebra?
A: The eigenvalue plays a crucial role in linear algebra since it helps in determining the properties of the transformation.
Q: What is the origin of the word "eigen"?
A: The word "eigen" comes from the German language, which means "own" or "typical."
Q: Can an eigenvector become a null vector after a transformation?
A: Yes, an eigenvector may become a null vector after undergoing a transformation.
