Ch 4.1: Vector Spaces and Subspaces
Vector Spaces and Subspaces 1
Vector Spaces and Subspaces 2
Matrix Spaces & Matrix Subspaces
Polynomial Subspaces
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Ch 4.2: Null, Column and Row Spaces
Bases for Col A & Row A & Null A
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Ch 4.3: Bases, Linearly Independent Sets
Basis for Vector Subspaces
Basis for Polynomial Subspaces
Basis for Matrix Subspaces
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Ch 4.4-5: Coordinate Systems
Coordinate Systems : Introduction
Coordinate Systems : Polynomials
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam like Question 4
Exam like Question 5
Ch 4.4-5:Coordinate Systems for Matrices
Coordinate Systems : Matrices 1
Coordinate Systems : Matrices 2
Coordinate Systems : Matrices 3
Coordinate Systems : Matrices 4
Ch 4.6: Change of Basis
Change of Basis : Vector Spaces
Change of Basis : Polynomials
Change of Basis: Matrices
Ch 5.4: Eigenvectors and Linear Transformations
Transformation Matrix Relative to Basis 1
Transformation Matrix Relative to Basis 2
Transformation Matrix Relative to Basis 3
Exam like Question 1
Exam like Question 2
Ch. 5.1-2: Eigenvalues and Eigenvectors
Eigenvalues & Eigenvectors : 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Algebraic and Geometric Multiplicities 1
Algebraic and Geometric Multiplicities-2
Eigenspace of Matrices
Ch. 5.3: Diagonalization
Diagonalization 1
Diagonalization 2
Exam like Question
Ch. 5.5: Complex Eigenvalues
Complex Eigenvalues I
Complex Eigenvalues II
Ch 6.1: Orthogonality
Key concepts for orthogonality
Orthogonal Complement
Orthagonal Complement 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam like Question 4
Ch 6.2: Orthogonal Sets and Bases
Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Orthonormal Sets and Basis
Orthogonal Matrix
Ch 6.3: Orthogonal Projections
Orthogonal Projection 1
Orthogonal Projection 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Ch 6.4: The Gram-Schmidt Process
The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
Exam like Question 1
Exam like Question 2
QR Factorization
QR Factorization
Exam like Question
Least Squares Solution & Approximation
Least Squares Solution
Exam like Question 1
Exam like Question 2
Sample Final Problems
Null & Column & Row Spaces
Null & Column & Row Spaces
Null & Column & Row Spaces
Null & Column & Row Spaces
Challenging: Null & Column & Row Spaces
Diagonalization 1
Diagonalization 2
Diagonalization 3
Diagonalization 4
The Gram-Schmidt Process
The Gram-Schmidt Process
The Gram-Schmidt Process
The Gram-Schmidt Process
QR Factorization
QR Factorization
Bonus Challenging Problem
(NEW) Spring 2024 Exam Problems
Polynomial Basis
Change of Basis
Eigenvectors & Diagonalization
Least Square Solution
Gram-Schmidt Process
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2016 senesinde başladığım Koç Üniversitesi Matematik bölümünden 2020 senesinde fakülte üçüncüsü olarak mezun oldum. Lisans ve yüksek lisans eğitimlerim boyunca çeşitli derslerde asistanlık yaptım. 2021'de Koç Üniversitesi'nde Matematik yüksek lisansına başladım ve 2023 yılında mezun oldum. Şimdi Michigan State Üniversitesi'nde doktora yapıyorum. Topoloji alanıyla ilgilenmekteyim.
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