When will I have access to the lectures and assignments?

To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

What will I get if I subscribe to this Specialization?

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.

Is financial aid available?

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

Linear Algebra: Orthogonality and Diagonalization

Ce cours n'est pas disponible en Français (France)

Nous sommes actuellement en train de le traduire dans plus de langues.

Linear Algebra: Orthogonality and Diagonalization

Ce cours fait partie de Spécialisation "Linear Algebra from Elementary to Advanced"

Instructeur : Joseph W. Cutrone, PhD

Enseignant de premier plan

4 095 déjà inscrits

Inclus avec

4 modules

Obtenez un aperçu d'un sujet et apprenez les principes fondamentaux.

49 avis

niveau Intermédiaire

Certaines connaissances prérequises

9 heures à compléter

Planning flexible

Apprenez à votre propre rythme

4 modules

Obtenez un aperçu d'un sujet et apprenez les principes fondamentaux.

49 avis

niveau Intermédiaire

Certaines connaissances prérequises

9 heures à compléter

Planning flexible

Apprenez à votre propre rythme

Compétences que vous acquerrez

Catégorie : Linear Algebra
Catégorie : Artificial Intelligence and Machine Learning (AI/ML)
Catégorie : Geometry
Catégorie : Applied Mathematics
Catégorie : Algebra

Détails à connaître

Certificat partageable

Ajouter à votre profil LinkedIn

Évaluations

11 devoirs

Enseigné en Anglais

91%

of learners achieved a positive career outcome

Découvrez comment les employés des entreprises prestigieuses maîtrisent des compétences recherchées

En savoir plus sur Coursera pour les affaires

logos de Petrobras, TATA, Danone, Capgemini, P&G et L'Oreal

Élaborez votre expertise du sujet

Ce cours fait partie de la Spécialisation "Linear Algebra from Elementary to Advanced"

Lorsque vous vous inscrivez à ce cours, vous êtes également inscrit(e) à cette Spécialisation.

Apprenez de nouveaux concepts auprès d'experts du secteur
Acquérez une compréhension de base d'un sujet ou d'un outil
Développez des compétences professionnelles avec des projets pratiques
Obtenez un certificat professionnel partageable

Il y a 4 modules dans ce cours

This is the third and final course in the Linear Algebra Specialization that focuses on the theory and computations that arise from working with orthogonal vectors. This includes the study of orthogonal transformation, orthogonal bases, and orthogonal transformations. The course culminates in the theory of symmetric matrices, linking the algebraic properties with their corresponding geometric equivalences. These matrices arise more often in applications than any other class of matrices.

The theory, skills and techniques learned in this course have applications to AI and machine learning. In these popular fields, often the driving engine behind the systems that are interpreting, training, and using external data is exactly the matrix analysis arising from the content in this course. Successful completion of this specialization will prepare students to take advanced courses in data science, AI, and mathematics.

Détails du module

In this module, we define a new operation on vectors called the dot product. This operation is a function that returns a scalar related to the angle between the vectors, distance between vectors, and length of vectors. After working through the theory and examples, we hone in on both unit (length one) and orthogonal (perpendicular) vectors. These special vectors will be pivotal in our course as we start to define linear transformations and special matrices that use only these vectors.

Inclus

2 vidéos2 lectures3 devoirs

In this module we will study the special type of transformation called the orthogonal projection. We have already seen the formula for the orthogonal projection onto a line so now we generalize the formula to the case of projection onto any subspace W. The formula will require basis vectors that are both orthogonal and normalize and we show, using the Gram-Schmidt Process, how to meet these requirements given any non-empty basis.

Inclus

3 vidéos3 lectures4 devoirs

3 vidéosTotal 51 minutes

Orthogonal Projections18 minutes
Gram-Schmidt Process14 minutes
Least-Squares Problems19 minutes

3 lecturesTotal 30 minutes

Orthogonal Projections10 minutes
Finding Orthogonal Bases10 minutes
Least-Squares Solutions10 minutes

4 devoirsTotal 120 minutes

Orthogonal Projections Practice30 minutes
Orthogonal Bases Practice30 minutes
Least-Squares Solutions Practice30 minutes
Orthogonal Projections and Least Squares30 minutes

In this module we look to diagonalize symmetric matrices. The symmetry displayed in the matrix A turns out to force a beautiful relationship between the eigenspaces. The corresponding eigenspaces turn out to be mutually orthogonal. After normalizing, these orthogonal eigenvectors give a very special basis of R^n with extremely useful applications to data science, machine learning, and image processing. We introduce the notion of quadratic forms, special functions of degree two on vectors , which use symmetric matrices in their definition. Quadratic forms are then completely classified based on the properties of their eigenvalues.

Inclus

2 vidéos2 lectures3 devoirs

Inclus

1 devoir

Obtenez un certificat professionnel

Ajoutez ce titre à votre profil LinkedIn, à votre curriculum vitae ou à votre CV. Partagez-le sur les médias sociaux et dans votre évaluation des performances.