Linear Algebra and Applications (Pengtao Xie)

Spaces

• Lecture 1: Vector Space (I)
• Lecture 2: Vector Space (II)
• Lecture 3: Inner-Product Space (I)
• Lecture 4: Inner-Product Space (II)
• Lecture 5: Reproducing Kernel Hilbert Space (I)
• Lecture 6: Reproducing Kernel Hilbert Space (II)

Matrices

• Lecture 7: Basics of Matrices (I)
• Lecture 8: Basics of Matrices (II)
• Lecture 9: Matrix Determinant (I)
• Lecture 10: Matrix Determinant (II)
• Lecture 11: Eigenvalue and Eigenvectors (I)
• Lecture 12: Eigenvalue and Eigenvectors (II)

Operators

• Lecture 13: Linear Transformations (I)
• Lecture 14: Linear Transformations (II)
• Lecture 15: Matrix Decomposition (I)
• Lecture 16: Matrix Decomposition (II)

Special Types of Matrices

• Lecture 17: Positive Semidefinite Matrices
• Lecture 18: Hermitian Matrices