eigenvalue
Matrix scaling factor
In linear algebra, an eigenvalue is a scalar that characterizes how a linear transformation stretches or compresses space along a particular direction.
When a matrix transforms a vector and the result points in the same direction as the original (possibly reversed), the factor by which it's scaled is the eigenvalue.
The concept appears throughout physics, engineering, and data science—in quantum mechanics, structural analysis, and principal component analysis.
The largest eigenvalue determines the system's dominant behavior.
Ordered numerical arrangement
- diagonalizationReducing to diagonal form
- characteristicDistinguishing quality or trait
- polynomialExpression with variable terms
- determinantMatrix-derived scalar quantity
multiplicity · scalar · decomposition · trace · transpose · symmetric · triangular · invertible
Continuous range of values
- principalChief school administrator
- dominantHaving superior influence
- leadingGuiding or pacing type
- largestMost big
smallest · positive · negative · real · complex · imaginary · conjugate · distinct
Operator-invariant quantum state
- operatorOne who works machinery
- observableCapable of being detected
- wavefunctionQuantum state's mathematical representation
- measurementDetermining size or amount
Schrödinger · energy · spin · superposition · collapse · degeneracy · perturbation · stationary
Relating to figures
- algorithmFinite problem-solving procedure
- iterationRepeated procedural pass
- QRTwo-dimensional scannable code
- solverOne who finds solutions
convergence · approximation · estimation · MATLAB · sparse · sensitivity · roundoff · stability
matrix
Ordered numerical arrangement
- diagonalizationReducing to diagonal form
- characteristicDistinguishing quality or trait
- polynomialExpression with variable terms
determinant · multiplicity · scalar · decomposition · trace · transpose · symmetric · triangular · invertible · coefficient
spectrum
Continuous range of values
largest · smallest · positive · negative · real · complex · imaginary · conjugate · distinct · repeated
eigenstate
Operator-invariant quantum state
- operatorOne who works machinery
- observableCapable of being detected
- wavefunctionQuantum state's mathematical representation
measurement · Schrödinger · energy · spin · superposition · collapse · degeneracy · perturbation · stationary · quantization
numerical
Relating to figures
- algorithmFinite problem-solving procedure
- iterationRepeated procedural pass
- QRTwo-dimensional scannable code
solver · convergence · approximation · estimation · MATLAB · sparse · sensitivity · roundoff · stability
- math conceptsangle, numbers, algebra, circle, equations
- linear algebramatrix, linear equation, vectors, linear function, matrices
- operator theoryoperator, adjoint, spectrum, kernel, range
- quantum physicsquantum mechanics, quantum superposition, quantum state, quantum states, quantum entanglement
- eigenvalueseigendecomposition, diagonalization, multiplicity
- quantum measurementmeasurement problem, observable, eigenstate, quantum state, observer effect