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eigenvalue
This term is used exclusively within the technical registers of linear algebra, quantum mechanics, and data science. It describes a specific scalar that characterizes how a linear transformation affects a particular vector, maintaining the vector's direction while altering its magnitude.
In practical application, eigenvalues are central to principal component analysis (PCA) and stability analysis in engineering. Because it is a specialized mathematical term, it is almost never encountered in general conversation or non-technical writing.
Meanings
A scalar value that is associated with a linear transformation, specifically one that represents the factor by which a corresponding eigenvector is scaled during that transformation.
Examples
This is an eigenvalue.
This is an eigenvalue.
He calculated the eigenvalue quickly.
He calculated the eigenvalue quickly.
The professor explained the eigenvalue during the lecture.
I wonder if this eigenvalue affects the system stability.
The detective noticed the eigenvalue in the encrypted code.
The lead engineer analyzed the eigenvalue for structural resonance.
Historically the concept of the eigenvalue revolutionized quantum mechanics.