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LİNEER CEBİR

  • Elementary marix
  • Permutation matrix
  • Bir Matrisin Transpozesi
  • Matris İşlemleri 
  • İlkel Satır ve Sütun İşlemleri
  • Bir Matrisin Basamak Biçimi
  • Br Matrisin Rankı
  • Vector spaces
  • Null spaces
  • Column and row spaces
  • Determinants
  • Lineer denklem sistemleri
  • Vektör uzayları 
  • Lineer transformations 
  • eigenvalues and eigenvectors ,
  • orthogonal vectors
  • Orthonormal vectors
  • orthogonal  , orthonormal projections
  • Diagonalizaion of vectors,
  • differensiyel of vectors
  • Genel tekrar ve alıştırmalar

1. Introduction to Vectors

1.1 Vectors and Linear Combinations
1.2 Lengths and Dot Products
1.3 Matrices

2. Solving Linear Equations

2.1 Vectors and Linear Equations
2.2 The Idea of Elimination
2.3 Elimination Using Matrices
2.4 Rules for Matrix Operations
2.5 Inverse Matrices
2.6 Elimination = Factorization: A = LU
2.7 Transposes and Permutations

3. Vector Spaces and Subspaces

3.1 Spaces of Vectors
3.2 The Nullspace of A: Solving Ax = 0
3.3 The Rank and the Row Reduced Form
3.4 The Complete Solution to Ax = b
3.5 Independence, Basis, and Dimension
3.6 Dimensions of the Four Subspaces

4. Orthogonality

4.1 Orthogonality of the Four Subspaces
4.2 Projections
4.3 Least Squares Approximations
4.4 Orthogonal Bases and Gram-Schmidt

5. Determinants

5.1 The Properties of Determinants
5.2 Permutations and Cofactors
5.3 Cramer's Rule, Inverses, and Volumes

6. Eigenvalues and Eigenvectors

6.1 Introduction to Eigenvalues
6.2 Diagonalizing a Matrix
6.3 Applications to Differential Equations
6.4 Symmetric Matrices
6.5 Positive Definite Matrices
6.6 Similar Matrices
6.7 Singular Value Decomposition (SVD)

7. Linear Transformations

7.1 The Idea of a Linear Transformation
7.2 The Matrix of a Linear Transformation
7.3 Diagonalization and the Pseudoinverse

8. Applications

8.1 Matrices in Engineering
8.2 Graphs and Networks
8.3 Markov Matrices, Population, and Economics
8.4 Linear Programming
8.5 Fourier Series: Linear Algebra for Functions
8.6 Linear Algebra for Statistics and Probability
8.7 Computer Graphics

9. Numerical Linear Algebra

9.1 Gaussian Elimination in Practice
9.2 Norms and Condition Numbers
9.3 Iterative Methods and Preconditioners

10. Complex Vectors and Complex Matrices

10.1 Complex Numbers
10.2 Hermitian and Unitary Matrices
10.3 The Fast Fourier Transform

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