Digital Audiovisual Lectures

Chapter 01: Introduction [MORE]

      • What is a row vector? [YOUTUBE 1:24]
      • What is a column vector? [YOUTUBE 1:58]
      • What is a square matrix? [YOUTUBE 1:44]
      • What is an upper triangular matrix? [YOUTUBE 3:02]
      • What is a lower triangular matrix? [YOUTUBE 3:14]
      • What is an identity matrix? [YOUTUBE 2:02]
      • Diagonally dominant matrix [YOUTUBE 7:22]

Chapter 02: Vectors [MORE]

      • What is a vector? [YOUTUBE 2:27]
      • What is a vector? Example [YOUTUBE 1:15]
      • When are two vectors equal? [YOUTUBE 2:02]
      • When are two vectors equal? Example [YOUTUBE 2:26]
      • How do you add two vectors? [YOUTUBE 1:34]
      • How do you add two vectors? Example [YOUTUBE 1:48]
      • What is a null (or zero) vector? [YOUTUBE 1:12]
      • What is a unit vector? [YOUTUBE 1:30]
      • What is a unit vector? Example [YOUTUBE 1:49]
      • How do you multiply a vector by a scalar? [YOUTUBE 1:18]
      • How do you multiply a vector by a scalar? Example [YOUTUBE 1:16]
      • What do you mean by linear combination of vectors? [YOUTUBE 1:44]
      • What do you mean by linear combination of vectors? Example [YOUTUBE 2:34]
      • What do you mean by vectors being linearly independent? [YOUTUBE 2:28]
      • Are these vectors linearly independent? Example 1 [YOUTUBE 3:17]
      • Are these vectors linearly independent? Example 2 [YOUTUBE 9:13]
      • What do you mean by rank of a set of vectors? [YOUTUBE 2:09]
      • Rank of a set of vectors: Example 1 [YOUTUBE 3:53]
      • Rank of a set of vectors: Example 2 [YOUTUBE 2:27]
      • Prove that if a set of vectors contains a null vector, the set of vectors is linearly dependent [YOUTUBE 2:29]
      • Prove that if a set of vectors is linearly independent, then a subset of it is also linearly independent [YOUTUBE 5:42]
      • Prove that if a set of vectors is linearly dependent, then at least one vector can be written as a linear combination of others [YOUTUBE 4:06]
      • How can vectors be used to write simultaneous linear equations? [YOUTUBE 5:08]
      • How can vectors be used to write simultaneous linear equations? Example [YOUTUBE 3:13]
      • What is the definition of the dot product of two vectors? [YOUTUBE 2:00]
      • Dot product of two vectors Example [YOUTUBE 1:41]

Chapter 03: Binary Matrix Operations [MORE]

      • Adding two matrices Theory [YOUTUBE 1:54]
      • Adding two matrices Example [YOUTUBE 2:11]
      • Subtracting two matrices Theory [YOUTUBE 1:40]
      • Subtracting two matrices Example [YOUTUBE 2:05]
      • Multiplying two matrices Theory [YOUTUBE 4:33]
      • Multiplying two matrices Example [YOUTUBE 6:20]
      • Product of a scalar and a matrix Theory [YOUTUBE 1:37]
      • Product of a scalar and a matrix Example [YOUTUBE 1:45]
      • Linear combination of matrices Theory [YOUTUBE 2:04]
      • Linear combination of matrices Example [YOUTUBE 3:57]
      • Rules of binary matrix operations Part 1 of 4 [YOUTUBE 1:47]
      • Rules of binary matrix operations Part 2 of 4 [YOUTUBE 1:38]
      • Rules of binary matrix operations Part 3 of 4 [YOUTUBE 2:50]
      • Rules of binary matrix operations Part 4 of 4 [YOUTUBE 2:31]
      • Is matrix multiplication commutative? [YOUTUBE 4:01]

Chapter 04: Unary Matrix Operations [MORE]

      • Transpose of a matrix [YOUTUBE 4:12]
      • Symmetric matrix [YOUTUBE 3:20]
      • Skew symmetric matrix [YOUTUBE 3:12]
      • Determinant of a matrix using minors Theory [YOUTUBE 4:41]
      • Determinant of a matrix using cofactors Theory [YOUTUBE 3:26]
      • Determinant of a matrix using minors Example [YOUTUBE 6:26]
      • Determinant of a matrix using cofactors Example [YOUTUBE 5:31]
      • Theorems on determinants Part 1 of 4 [YOUTUBE 1:36]
      • Theorems on determinants Part 2 of 4 [YOUTUBE 3:35]
      • Theorems on determinants Part 3 of 4 [YOUTUBE 3:21]
      • Theorems on determinants Part 4 of 4 [YOUTUBE 2:42]

Chapter 05: System of Equations [MORE]

      • A real life problem of setting up simultaneous linear equations [YOUTUBE 5:23]
      • Writing simultaneous linear equations in matrix form [YOUTUBE 5:25]
      • Consistent and inconsistent system of equations Theory [YOUTUBE 2:56]
      • Consistent and inconsistent system of equations Example [YOUTUBE 5:31]
      • Rank of a matrix Definition [YOUTUBE 1:21]
      • Rank of a matrix Example 1 [YOUTUBE 1:31]
      • Rank of a matrix Example 2 [YOUTUBE 2:50]
      • Distinguishing between consistent and inconsistent system of equations based on rank of matrices [YOUTUBE 3:06]
      • Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 1 [YOUTUBE 4:15]
      • Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 2 [YOUTUBE 8:42]
      • Distinguishing between consistent and inconsistent system of equations based on rank of matrices Example 3 [YOUTUBE 6:07]
      • If a solution exists, how do we know if it is unique? [YOUTUBE 3:25]
      • Does a set of equations have a unique solution? Example 1 [YOUTUBE 2:18]
      • Does a set of equations have a unique solution? Example 2 [YOUTUBE 2:23]
      • If we have more equations than unknowns, does it mean we have inconsistent system of equations? [YOUTUBE 8:11]
      • Can a system of equations have more then one but not infinite number of solutions? [YOUTUBE 4:57]
      • Can we divide two matrices? [YOUTUBE 5:39]
      • Some statements about the inverse of matrices [YOUTUBE 2:53]
      • Inverse of matrices Example [YOUTUBE 3:40]
      • Using concept of inverse to solve a set of equations [YOUTUBE 2:27]
      • Finding the inverse of a matrix Theory [YOUTUBE 4:32]
      • Finding the inverse of a matrix Example [YOUTUBE 7:03]
      • Finding the inverse of a matrix by adjoints Theory [YOUTUBE 2:15]
      • Finding the inverse of a matrix by adjoints Example [YOUTUBE 7:19]
      • If the inverse of [A] exists, is it unique? [YOUTUBE 2:30]

Chapter 06: Gaussian Elimination [MORE]

      • Naive Gaussian elimination: Theory: Part 1 of 2 [YOUTUBE 10:27]
      • Naive Gaussian elimination: Theory: Part 2 of 2 [YOUTUBE 2:22]
      • Naive Gauss Elimination Method: Example: Part 1 of 2 (Forward Elimination) [YOUTUBE 10:49]
      • Naive Gauss Elimination Method: Example: Part 2 of 2 (Back Substitution) [YOUTUBE 6:40]
      • Pitfalls of Naive Gauss Elimination Method: [YOUTUBE 7:20]
      • Naive Gauss Elimination: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 7:20]
      • Naive Gauss Elimination: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 7:40]
      • Naive Gauss Elimination: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 8:07]
      • Gaussian Elimination With Partial Pivoting: Theory [YOUTUBE 10:39]
      • Gaussian Elimination With Partial Pivoting: Example: Part 1 of 3 (Forward Elimination) [YOUTUBE 7:15]
      • Gaussian Elimination With Partial Pivoting: Example: Part 2 of 3 (Forward Elimination) [YOUTUBE 10:08]
      • Gaussian Elimination With Partial Pivoting: Example: Part 3 of 3 (Back Substitution) [YOUTUBE 6:18]
      • Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 1 of 3 [YOUTUBE 8:58]
      • Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 2 of 3 [YOUTUBE 8:17]
      • Gaussian Elimination With Partial Pivoting: Round-off Error Issues: Example: Part 3 of 3 [YOUTUBE 5:48]
      • Determinant of a Matrix Using Forward Elimination Method: Background [YOUTUBE 5:17]
      • Determinant of a Matrix Using Forward Elimination Method: Example [YOUTUBE 10:07]

Chapter 07: LU Decomposition [MORE]

      • LU Decomposition: Basis [YOUTUBE 9:02]
      • LU Decomposition Method: Example [YOUTUBE 10:29]
      • Why LU Decomposition: Part 1 [YOUTUBE 4:58]
      • Why LU Decomposition: Part 2 [YOUTUBE 8:05]
      • Decomposing a Square Matrix: Part 1 of 2 [YOUTUBE 6:56]
      • Decomposing a Square Matrix: Part 2 of 2 [YOUTUBE 4:37]
      • Finding Inverse of a Matrix Using LU Decomposition: Background [YOUTUBE 6:03]
      • Finding Inverse of a Matrix Using LU Decomposition: Example [YOUTUBE 10:20]

Chapter 08: Gauss-Seidel Method [MORE]

      • Gauss-Seidel Method of Solving Simul Linear Eqns: Theory: Part 1 of 2 [YOUTUBE 8:01]
      • Gauss-Seidel Method of Solving Simul Linear Eqns: Theory: Part 2 of 2 [YOUTUBE 5:38]
      • Gauss-Seidel Method of Solving Simul Linear Eqns: Example: Part 1 of 2 [YOUTUBE 9:17]
      • Gauss-Seidel Method of Solving Simul Linear Eqns: Example: Part 2 of 2 [YOUTUBE 7:40]
      • Gauss-Seidel Method of Solving Simul Linear Eqns: Pitfalls and Advantages: Part 1 of 2 [YOUTUBE 7:50]
      • Gauss-Seidel Method of Solving Simul Linear Eqns: Pitfalls and Advantages: Part 2 of 2 [YOUTUBE 8:14]

Chapter 09: Adequacy of Solutions [MORE]

      • Ill-conditioned and well-conditioned system of equations [YOUTUBE 10:12]
      • Row sum norm of a matrix Theory [YOUTUBE 2:34]
      • Row sum norm of a matrix Example [YOUTUBE 3:06]
      • How is the norm related to the conditioning of a system of equations Part 1 of 2 [YOUTUBE 8:55]
      • How is the norm related to the conditioning of a system of equations Part 2 of 2 [YOUTUBE 5:58]
      • Properties of norms [YOUTUBE 3:37]
      • Relating changes in coefficient matrix to changes in solution vector [YOUTUBE 4:18]
      • Relating changes in coefficient matrix to changes in solution vector Proof [YOUTUBE 8:46]
      • Relating changes in right hand side vector to changes in solution vector [YOUTUBE 3:12]
      • Number of significant digits correct in my solution vector Theory [YOUTUBE 4:00]
      • Number of significant digits correct in my solution vector Example 1 [YOUTUBE 3:57]
      • Number of significant digits correct in my solution vector Example 2 [YOUTUBE 4:26]

Chapter 10: Eigenvalues and Eigenvectors [MORE]

      • What is the origin of the word eigenvalue [YOUTUBE 1:02]
      • A physical example of application of eigenvalues and eigenvectors [YOUTUBE 16:23]
      • Definition of eigenvalues and eigenvectors [YOUTUBE 3:11]
      • How do I find eigenvalues of a square matrix [YOUTUBE 4:33]
      • How do I find eigenvalues of a square matrix? Example [YOUTUBE 3:46]
      • How do I find eigenvectors of a square matrix? Example [YOUTUBE 6:33]
      • How do I find eigenvectors of a square matrix? Example 2 [YOUTUBE 13:10]
      • Theorems of eigenvalues and eigenvectors Part 1 of 6 [YOUTUBE 2:19]
      • Theorems of eigenvalues and eigenvectors Part 2 of 6 [YOUTUBE 2:06]
      • Theorems of eigenvalues and eigenvectors Part 3 of 6 [YOUTUBE 2:43]
      • Theorems of eigenvalues and eigenvectors Part 4 of 6 [YOUTUBE 0:53]
      • Theorems of eigenvalues and eigenvectors Part 5 of 6 [YOUTUBE 1:37]
      • Theorems of eigenvalues and eigenvectors Part 6 of 6 [YOUTUBE 3:15]
      • How does one find eigenvalues and eigenvectors numerically [YOUTUBE 4:57]
      • How does one find eigenvalues and eigenvectors numerically Example [YOUTUBE 8:09]