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ertagon2
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An eigenvector is a vector in a given vector space that remains unchanged when multiplied by a particular matrix. It is a special type of vector that represents the direction of the transformation caused by the matrix.
The term "eigen" comes from the German word "eigen" which means "own" or "inherent." In mathematics, an eigenvector is a vector that is inherent to a particular matrix and remains unchanged when multiplied by that matrix.
Eigenvectors are important in linear algebra because they provide a way to simplify complicated matrix operations and understand the behavior of linear transformations. They also have applications in fields such as physics, engineering, and computer science.
To find eigenvectors, you first need to find the eigenvalues of the matrix. Then, for each eigenvalue, you solve a system of equations to find the corresponding eigenvector. This can be done using methods such as Gaussian elimination or by using software like MATLAB or Python.
There is no difference between an eigenvector and a characteristic vector. They both refer to the same type of vector that remains unchanged when multiplied by a particular matrix. However, the term "eigenvector" is more commonly used in mathematics, while "characteristic vector" is more commonly used in physics and engineering.