Eigenvalues Courses and Certifications

NPTEL-NOC IITM

Strongly Regular Graphs - Their Eigenvalues and Characterization

Discover strongly regular graphs through eigenvalue calculations and mathematical characterization techniques in this focused mathematical exploration.

• YouTube
• 31 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Positive Semi-Definite Matrices and the Eigenvalues of Their Partitioned Form

Explore the relationship between eigenvalues of positive semi-definite matrices and their partitioned blocks, focusing on non-negative eigenvalue properties.

• YouTube
• 24 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

The Eigenvalues of a Symmetric Matrix in Partitioned Form

Discover inequalities governing eigenvalues of symmetric matrices when expressed in partitioned block form through mathematical analysis and proofs.

• YouTube
• 21 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

The Rank of a Symmetric Matrix Equals the Number of Nonzero Eigenvalues

Discover how symmetric matrix rank equals nonzero eigenvalues count, exploring complete graph and bipartite graph eigenvalue properties in linear algebra.

• YouTube
• 21 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Bipartite Graphs and Their Eigenvalues

Discover the fundamental relationship between bipartite graph structure and eigenvalue symmetry around zero in this concise mathematical exploration.

• YouTube
• 21 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Eigenvalues of a Graph and Its Subgraph - A Relation Between the Largest Eigenvalue and the Degree(s)

Explore the relationship between graph eigenvalues and vertex degrees, including subgraph properties and bounds involving maximum and average degrees.

• YouTube
• 28 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

A Bound on the Diameter of a Graph Using the Number of Distinct Eigenvalues

Discover how graph diameter relates to distinct eigenvalues of adjacency matrices through mathematical bounds and proofs.

• YouTube
• 31 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Introduction to Eigenvalues and Eigenvectors

Discover eigenvalues and eigenvectors fundamentals, exploring how distinct eigenvalues yield independent eigenvectors and symmetric matrices produce real eigenvalues with orthogonal eigenvectors.

• YouTube
• 35 minutes
• On-Demand
• Free Video

For the Love of Physics

Quantum Harmonic Oscillator - Analytic Method for Eigenvalues and Eigenfunctions

Master the complete mathematical derivation of quantum harmonic oscillator eigenvalues and eigenfunctions using Schrödinger's equation and analytic methods.

• YouTube
• 1 hour 33 minutes
• On-Demand
• Free Video

Wrath of Math

Power Method for Dominant Eigenvalues and Eigenvectors in Linear Algebra

Learn to approximate dominant eigenvalues and eigenvectors using the power method with maximum entry and Euclidean scaling. Explore power sequences, Rayleigh quotient, and geometric intuition in linear algebra.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Squid: Schools for Quantum Information Development

Improved Approximations for Extremal Eigenvalues of Sparse Hamiltonians

Discover advanced approximation techniques for eigenvalues in sparse Hamiltonians, exploring new methods for quantum systems with q-local terms and improved mathematical approaches for k-sparse configurations.

• YouTube
• 24 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Quadratic Differentials and Degenerate Eigenvalues

Explore the relationship between quadratic differentials and degenerate eigenvalues in discrete integrable systems through advanced mathematical concepts and theoretical physics applications.

• YouTube
• 26 minutes
• On-Demand
• Free Video

AutoML Seminars

Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues

Delve into groundbreaking research on improving Linear RNNs' capabilities through negative eigenvalues, enhancing their performance in state-tracking tasks and language modeling applications.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Simons Foundation

Distribution of Zeros, Eigenvalues and Eigenfunctions in Number Theory

Explore statistical laws governing zeta functions and automorphic forms, examining numerical observations and their impact on arithmetical invariants in number theory.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Navigating Data Simplification with PCA

Master dimensionality reduction techniques using Principal Component Analysis (PCA) with Python's Scikit-learn, from basic concepts to practical implementation in machine learning projects.

• CodeSignal
• 3 hours
• On-Demand
• Free Certificate