What question did this study set out to answer?

Establish a rigorous algebraic foundation for approximating complex matrices using lower-rank representations derived from latent roots.

March 1, 1938American Mathematical Monthly

Matrix Approximation and Latent Roots

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Authors

AHA. S. HouseholderInstitute of Mathematical Statistics GYGale YoungOlivet College

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Implication

Theoretical analysis demonstrates low-rank matrix approximation via latent roots in linear systems, highlighting optimal dimension-reduction strategies.

Key Points

Establish a rigorous algebraic foundation for approximating complex matrices using lower-rank representations derived from latent roots.
Applied algebraic transformations and spectral decomposition to evaluate finite-dimensional matrices.
Analyzed residual approximation error bounds as functions of excluded latent roots.
Proved that truncating latent roots yields the optimal lower-rank matrix approximation under least-squares criteria.
Provided an exact mathematical formulation linking latent root magnitudes directly to matrix reconstruction error.

Cite This Study

Householder et al. (1938) studied this question.

synapsesocial.com/papers/6a0da2a4e9dfe5e7c4ba6736 https://doi.org/10.1080/00029890.1938.11990787

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Implication

Theoretical analysis demonstrates low-rank matrix approximation via latent roots in linear systems, highlighting optimal dimension-reduction strategies.

Matrix Approximation and Latent Roots

Discussion

Member takes

Implication

Key Points

Cite This Study

Matrix Approximation and Latent Roots

Discussion

Member takes

Implication

Key Points

Cite This Study

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