Lec 27 | MIT 18.06 Linear Algebra, Spring 2005
Lecture 27: Positive Definite Matrices and Minima. View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
Positive Definite Matrices and Minima | MIT 18.06SC Linear Algebra, Fall 2011
Positive Definite Matrices and Minima Instructor: Martina Balagovic View the complete course: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
mit- Length: 12:50
- Views: 952
- Tags: linear algebra positive definite matrices minima
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Positive Definite Matrix of an Inner Product
- refrigeratormathprof
- Length: 3:35
- Views: 391
- Tags: positive definite matrix
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Positive Semi-Definite Matrix 1: Square Root
Matrix Theory: Let A be an nxn matrix with complex entries. Assume that A is (Hermitian) positive semi-definite. We show that A has a unique (Hermitian) positive definite square root; that is, a PSD matrix S such that S^2 = A. The key ingredient is the Spectral Theorem for C^n. Example in Part 2.
Lecture 16: Positive Definite Matrices
In Lecture 16 we take a look at positive definite matrices, and some of the many areas in which they arise.
- ucmath352
- Length: 44:05
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- Tags: +lecture +mathematics +linear algebra
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Positive Semi-Definite Matrix 3: Factorization of Invertible Matrices
Matrix Theory: Let A be an invertible nxn matrix with complex entries. Using the square root result from Part 1, we show that A factors uniquely as PX, where P is unitary and X is (Hermitian) positive definite.
Positive Semi-Definite Matrix 2: Spectral Theorem
Matrix Theory: Following Part 1, we note the recipe for constructing a (Hermitian) PSD matrix and provide a concrete example of the PSD square root. We prove the Spectral Theorem for C^n in the remaining 9 minutes.
Lec 7 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 07: Positive definite day! License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
- mit
- Length: 52:56
- Views: 8024
- Tags: linear algebra networks Lagrange multipliers differential equations of equilibrium Laplace's equation potential flow boundary-value problems Fourier series discrete transform convolution
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Metric Tensor Part 1.wmv
What is the Metric Tensor | Linear Space | Vector Space | Dual Space | Dual Basis | Positive Definite Bi-linear Functional | Contravariant } Covariant Components of Vectors | Topological Space Topological Group Normed Linear Space Metric Space Inner product Euclidean Space Matrix Representation o...
Lecture 23: Simultaneous Linear Equations: Cholesky Method Part 1 of 4
Simultaneous Linear Equations: Cholesky Method : Solving Simultaneous Linear Equations (or SLE) [A] * {x} = {b}, by Cholesky method. Definition of Symmetric Positive Definite (or SPD). How to find the factorized/upper triangular matrix [U] ?? Definition of "fill-in" terms (during the factorizatio...
Lec 6 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 06: Eigenvalues (part 2); positive definite (part 1) License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
- mit
- Length: 50:19
- Views: 10587
- Tags: linear algebra networks Lagrange multipliers differential equations of equilibrium Laplace's equation potential flow boundary-value problems Fourier series discrete transform convolution
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Lec 34 | MIT 18.06 Linear Algebra, Spring 2005
Lecture 34: Final Course Review. View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
Lec 9 | MIT 18.06 Linear Algebra, Spring 2005
Lecture 9: Independence, Basis, and Dimension. View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
Lec 1 | MIT 18.085 Computational Science and Engineering I
Positive definite matrices K = A'CA A more recent version of this course is available at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu
- mit
- Length: 59:50
- Views: 65761
- Tags: mit opencourseware linear algebra engineering laplace differential lagrange convolution fourier boundary-value
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Lecture 24: Simultaneous Linear Equations: LDL Transpose Method Part 1 of 3
Simultaneous Linear Equations: LDL Transpose Method : Solving Simultaneous Linear Equations (or SLE) [A] * {x} = {b}, by L*D*L_transpose method. Definition of Symmetric Positive/Negative Definite. How to find the factorized lower triangular matrix [L] (with 1 on the diagonal terms) and the Diagon...
Lecture 23: Simultaneous Linear Equations: Cholesky Method Part 2 of 4
Simultaneous Linear Equations: Cholesky Method: Solving Simultaneous Linear Equations (or SLE) [A] * {x} = {b}, by Cholesky method. How to find the Cholesky factorized/upper triangular matrix by "graphical approach" ?? Numerical examples about SPD matrix. Forward solution phase.
Lec 25 | MIT 18.06 Linear Algebra, Spring 2005
Lecture 25: Symmetric Matrices and Positive Definiteness.* * NOTE: the audio is in the right channel only. If you here no audio, you are listening only to the left channel. View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ...
Lecture 23: Simultaneous Linear Equations: Cholesky Method Part 4 of 4
Simultaneous Linear Equations: Cholesky Method: Solving Simultaneous Linear Equations (or SLE) [A] * {x} = {b}, by Cholesky method. A complete 3x3 numerical example for Cholesky method: factorization, forward and backward phases.
Lecture 17: Cholesky Factorization
In Lecture 17 we look at the Cholesky factorisation and how we can use it to efficiently solve linear systems when the matrix A is positive definite, and how computing the factorisation is in itself t
Lecture 1b, Linear algebra refresh:
Lecture course 236330, Introduction to Optimization, by Michael Zibulevsky, Technion Linear and affine subspace; 0:0 (slides 05:39, 07:07 Lp norm of a vector 7:24 (slides 9:44 13:45 Matrix norms - 14:52 (slides 18:29) Inner product of matrices - 19:30 (slides 22:40) Eigenvalue decomposition -23:1...
- technion
- Length: 45:42
- Views: 341
- Tags: Introduction to Optimization Optimization Michael Zibulevsky 236330 cs
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