eigenvalues
Characteristic equation solutions
Eigenvalues are special numbers associated with a matrix or linear transformation.
When a transformation is applied to certain vectors (eigenvectors), it only stretches or shrinks them without changing their direction—the eigenvalue is the factor by which they're scaled.
The eigenvalues of this matrix are 3 and -1.
Eigenvalues appear throughout physics, engineering, and data analysis, revealing fundamental properties of systems—from vibration frequencies to principal components in statistics.
Reducing to diagonal form
- determinantMatrix-derived scalar quantity
- traceMinute remnant or pursue
- spectrumContinuous range of values
- orthogonalityState of being independent
Rapid oscillating movement
- oscillationRepeated back-and-forth movement
- resonanceAmplified oscillation at natural frequency
- frequencyRate of recurrence
- dampingDissipation of vibrational energy
harmonic · natural frequency · mechanical systems · standing waves · amplitude · phase
One who works machinery
- Schrödinger equationGoverns quantum state evolution
- energy levelsGradations of physical vitality
- observableCapable of being detected
- measurementDetermining size or amount
wavefunction · eigenstate · spectral lines · commutator · degeneracy · hydrogen atom · spin · angular momentum
State of balance
- control systemsMechanisms maintaining desired outputs
- feedbackReturned response data
- polesLong sticks or extremities
- asymptoticApproaching a limit infinitely
bifurcation · linearization · attractor · instability · steady-state · robustness · controllability · observability
Statistical dimension reduction
- varianceSpread around the mean
- loadingsAdded amounts or weights
- multivariateInvolving multiple variables simultaneously
- clusteringForming concentrated groups
machine learning · pattern recognition · compression · noise reduction
State of being linked
- centralityCore significance or position
- PageRankLink-based webpage ordering method
- networkInterconnected system
- random walkChance-governed sequential movement
diagonalization
Reducing to diagonal form
- determinantMatrix-derived scalar quantity
- traceMinute remnant or pursue
- spectrumContinuous range of values
orthogonality · unitary matrix · definiteness · rank · nullity
vibration
Rapid oscillating movement
- oscillationRepeated back-and-forth movement
- resonanceAmplified oscillation at natural frequency
- frequencyRate of recurrence
damping · harmonic · natural frequency · mechanical systems · standing waves · amplitude · phase
operator
One who works machinery
- Schrödinger equationGoverns quantum state evolution
- energy levelsGradations of physical vitality
- observableCapable of being detected
measurement · wavefunction · eigenstate · spectral lines · commutator · degeneracy · hydrogen atom · spin · angular momentum
equilibrium
State of balance
- control systemsMechanisms maintaining desired outputs
- feedbackReturned response data
- polesLong sticks or extremities
asymptotic · bifurcation · linearization · attractor · instability · steady-state · robustness · controllability · observability
PCA
Statistical dimension reduction
- varianceSpread around the mean
- loadingsAdded amounts or weights
- multivariateInvolving multiple variables simultaneously
clustering · machine learning · pattern recognition · compression · noise reduction
connectivity
State of being linked
- centralityCore significance or position
- PageRankLink-based webpage ordering method
- networkInterconnected system
- rootstaproot, root system, root tip, fibrous root, primary root
- Engineering Mathcalculus, algebra, linear algebra, differential equations, matrices
- linear algebramatrix, linear equation, vectors, linear function, matrices
- Quantum Mechanicssuperposition, entanglement, wave function, uncertainty principle, Schrodinger equation
- computational mathalgorithm, linear algebra, calculus, differential equations, finite element
- dimensionality reductionPCA, loading, component, factors, embedding