Orthogonality Courses and Certifications

Linear Algebra: Orthogonality and Diagonalization

55 ratings at Coursera

Compute dot products, build orthonormal bases with the Gram-Schmidt process, solve least squares problems, and diagonalize symmetric matrices to classify quadratic forms by eigenvalue properties.

• Coursera
• 4 weeks, 2 hours a week
• Self-Paced
• Paid Course

Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD

5 ratings at edX

This course takes you through roughly five weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.

• edX
• 3 weeks, 5-6 hours a week
• Self-Paced
• Free Online Course (Audit)

Orthogonality

Explores orthogonality through projections, Gram–Schmidt, least squares, QR decomposition, regression, and Fourier series.

• YouTube
• 3 hours 30 minutes
• Self-Paced
• Free Video

Khan Academy

Representing Vectors in RN Using Subspace Members - Linear Algebra - Khan Academy

Learn to represent any vector in Rⁿ uniquely as the sum of a vector in a subspace and one in its orthogonal complement.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Tom Rocks Maths

Oxford Linear Algebra - Inner Product Space

Explore inner product spaces, bilinear forms, and orthonormal sets in linear algebra. Learn key concepts and proofs with practical examples and exercises to enhance understanding.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Tensor Analysis - Lowering Index Operations, Inner Products, and Vector Norms - II

Discover tensor operations including index lowering, vector inner products, and norm calculations in this focused mathematical exploration.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Orthogonality of Signals - Lecture 10

Explore orthogonality of signals, a fundamental concept in signal processing and communication systems. Gain insights into its applications and importance.

• YouTube
• 16 minutes
• Self-Paced
• Free Video

Tobias Osborne

Symmetries and Quantum Mechanics - Orthogonality Relations for Characters - Lecture 5

Explore the fundamental principles of group representation theory in quantum mechanics, focusing on character orthogonality relations and their applications in quantum states.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Legendre Polynomials: Rodrigues Formula, Orthogonality, and Normalization Integral - Lecture 48

Explore Legendre polynomials, including Rodrigues formula, orthogonality, and normalization integral, to enhance your mathematical understanding.

• YouTube
• 19 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Orthogonality and Conjugacy

Explore orthogonality and conjugacy concepts in gradient methods, focusing on quadratic form visualization, conjugate directions, and their mathematical relationships.

• YouTube
• 12 minutes
• Self-Paced
• Free Video

Career Certificate

Applications of Linear Algebra

1 rating

Apply determinants, eigenvalues and eigenvectors to discrete dynamical systems and Markov chains, then use least-squares approximation, orthogonality, symmetric matrices and the singular value decomposition.

• edX
• 6 weeks, 5-6 hours a week
• Self-Paced
• $498.00
• 2 courses

Wrath of Math

Elementary Linear Algebra - Complete Course

Master matrix operations, vector spaces, eigenvalues, and transformations through comprehensive lessons covering Gaussian elimination, determinants, orthogonality, and advanced topics.

• YouTube
• 17 hours 13 minutes
• Self-Paced
• Free Video

Advanced Linear Algebra: Foundations to Frontiers

Build practical algorithms for matrix computations: orthogonalization, solving linear systems, and eigenvalues and eigenvectors, while analyzing the effects of floating-point arithmetic on computed results.

• edX
• 16 weeks, 8-12 hours a week
• Self-Paced
• Free Online Course (Audit)

Linear Algebra I: Vectors and Linear Equations

5 ratings at edX

This course provides an overview of bachelor-level linear algebra. You will review all the concepts and practice and refresh the skills related to vectors and linear equations.

• edX
• 6 weeks, 4-6 hours a week
• Self-Paced
• Free Online Course (Audit)

AI Engineer

Surfacing Semantic Orthogonality Across Model Safety Benchmarks - A Multi-Dimensional Analysis

Explore semantic clustering analysis of AI safety benchmarks, revealing distinct harm categories and coverage gaps across five open-source datasets using UMAP and k-means clustering techniques.

• YouTube
• 27 minutes
• Self-Paced
• Free Video