What is an Eigenvalue and an Eigenvector?
In: Mathematics
Trying to keep it ELI5 but not be patronizing in simplicity. Vectors are a clever way to communicate magnitude and direction. The classic example is a force vector. You can draw an arrow where the direction the arrow is pointing indicates the direction of the force, and the length of the arrow indicates the size or magnitude of the force. Matrices are a good way of organizing the relevant data to construct one.
Eigen values and Eigen vectors are fancy types of matrices that you can use in a branch of mathematics called linear algebra. Essentially, an eigen vector is a type of vector that you can multiply an existing vector by…that doesn’t change the existing vector’s direction. It only changes its magnitude. And the Eigen value is the scalar factor of that change of magnitude.
They’re neat principles of mathematics that have applications all over the place. I use them in my career when it comes to random vibration analysis of aerospace components. When we find natural frequencies of a vibrating object those frequencies are actually eigenvalues of the system of equations that we’re solving.
They have lots of different uses in all sorts of complicated things but the general knowledge is quite simple. It’s a vector that when multiplied by an existing vector, it only changes the magnitude, and the scale of that magnitude change is an eigen value.
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