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Pseudo Epsilon
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can someone PLEASE explain eigenvalues and eigenvectors and how to calculate them or a link to a site that teaches it simply?
That is sad to hear, eigenvectors and eigenvalues are very basic maths. Teachers are very underqualified these days.Pseudo Epsilon said:Ive already read the wiki and asked my math teacher, he doesn't even know what they are.
Eigenvalues and eigenvectors are concepts in linear algebra that are used to describe certain properties of a square matrix. Eigenvalues are scalar values that represent the amount by which an eigenvector is scaled when it is multiplied by the matrix. Eigenvectors are non-zero vectors that remain in the same direction when multiplied by the matrix.
Eigenvalues and eigenvectors are calculated by finding the roots of the characteristic polynomial of the matrix. The characteristic polynomial is obtained by subtracting the identity matrix multiplied by a scalar from the original matrix and then finding the determinant of the resulting matrix.
Eigenvalues and eigenvectors are important because they provide insight into the behavior of a matrix. They are used to solve systems of linear equations, analyze systems of differential equations, and perform transformations in linear algebra.
Yes, a matrix can have multiple eigenvalues. However, each eigenvalue will correspond to a unique eigenvector. This means that the number of eigenvalues a matrix has is equal to the number of eigenvectors.
Eigenvalues and eigenvectors are commonly used in data analysis for dimensionality reduction and feature extraction. They can also be used to identify patterns and relationships between variables in a dataset.