Subspaces Courses and Certifications

Linear Algebra

8 reviews

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

• MIT OpenCourseWare
• 36 hours
• On-Demand
• Free Video

Discover AI

AI Learns in Low-Curvature Subspaces - RLVR

Uncover how reinforcement learning fine-tuning achieves dramatic reasoning gains through geometric optimization bias, revealing the "Three-Gate Theory" behind sparse parameter updates.

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

Discover AI

The Eigenvectors of AI - Shared LoRA Subspaces for Continual Learning

Explore shared LoRA subspaces for continual learning, examining eigenvector approaches to prevent catastrophic forgetting in AI systems through innovative parameter-efficient methods.

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

Wrath of Math

Orthogonal Projections on Inner Product Subspaces - Linear Algebra

Explore orthogonal projections in inner product spaces, including the projection theorem and methods for calculating projections onto subspaces and orthogonal components.

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

Khan Academy

Linear Subspaces - Vectors and Spaces - Linear Algebra

Explore linear subspaces in Rn, a fundamental concept in linear algebra. Learn to visualize and understand multi-dimensional mathematical reasoning through vectors, matrices, and transformations.

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

Linear Algebra: Matrix Algebra, Determinants, & Eigenvectors

76 ratings at Coursera

Develop matrix algebra techniques, study determinants, and explore eigenvectors to analyze linear transformations. Apply concepts to Markov chains and Google PageRank algorithm.

• Coursera
• 14 hours 53 minutes
• On-Demand
• Paid Course

The Four Fundamental Subspaces and Least Squares

Explore the four fundamental subspaces of linear algebra with Gilbert Strang, understanding column spaces, nullspaces, and how to find the best solution when a matrix isn't invertible using the pseudoinverse concept.

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

Steve Brunton

Koopman Observable Subspaces and Finite Linear Representations of Nonlinear Dynamics for Control

Explore Koopman operator theory for simulating and controlling nonlinear dynamical systems using linear representations, with applications in optimal control and system analysis.

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

Simons Institute

Subspace Clustering Using Ensembles of K-Subspaces

Explore subspace clustering techniques, focusing on K-Subspaces ensembles. Learn about applications, results, and comparisons with other algorithms in this insightful talk by Laura Balzano.

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

NPTEL-NOC IITM

Invariant Subspaces, Eigenvalues, and Eigenvectors

Explore invariant subspaces, eigenvalues, and eigenvectors to deepen your understanding of linear algebra concepts and their applications.

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

Discover AI

Mixture of Expert MoE - Spectral Decomposition in Orthogonal Subspaces

Discover breakthrough SD-MoE architecture using spectral decomposition for superior expert specialization, addressing why current MoE models underperform against proprietary LLMs.

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

Fields Institute

Shift Invariant Subspaces of Composition Operators

Explore shift invariant subspaces of composition operators in analytic function spaces, focusing on their properties and applications in mathematical analysis.

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

Centre de recherches mathématiques - CRM

Arithmeticity and FC-Subspaces of Hyperbolic Manifolds

Explore connections between geometry and arithmeticity of hyperbolic orbifolds using fc-subspaces. Learn about new arithmeticity criteria and applications to reflection groups and hyperbolic link complements.

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

Centre de recherches mathématiques - CRM

Nullstellensatz-Inspired Algorithms for Certifying Entanglement of Subspaces

Explore Nullstellensatz-inspired algorithms for certifying entanglement in quantum subspaces. Delve into computational techniques, applications, and extensions to general varieties.

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

Centrum Fizyki Teoretycznej PAN

All Genuinely Entangled Stabilizer Subspaces are Multipartite Fully Nonlocal

Explore the equivalence between genuine entanglement and nonlocality in stabilizer states, revealing insights into quantum information processing and device-independent frameworks.

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