Determinants | Analytic geometry | Matrices
In linear algebra, the Gram matrix (or Gramian matrix, Gramian) of a set of vectors in an inner product space is the Hermitian matrix of inner products, whose entries are given by the inner product . If the vectors are the columns of matrix then the Gram matrix is in the general case that the vector coordinates are complex numbers, which simplifies to for the case that the vector coordinates are real numbers. An important application is to compute linear independence: a set of vectors are linearly independent if and only if the (the determinant of the Gram matrix) is non-zero. It is named after Jørgen Pedersen Gram. (Wikipedia).
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Understanding Matrices and Matrix Notation
In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start
From playlist Mathematics (All Of It)
Example of Gram-Schmidt Orthogonalization
Linear Algebra: Construct an orthonormal basis of R^3 by applying the Gram-Schmidt orthogonalization process to (1, 1, 1), (1, 0, 1), and (1, 1, 0). In addition, we show how the Gram-Schmidt equations allow one to factor an invertible matrix into an orthogonal matrix times an upper tria
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Matrix Addition, Subtraction, and Scalar Multiplication
This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
N-grams | Introduction to Text Analytics with R Part 6
N-grams includes specific coverage of: • Validate the effectiveness of TF-IDF in improving model accuracy. • Introduce the concept of N-grams as an extension to the bag-of-words model to allow for word ordering. • Discuss the trade-offs involved of N-grams and how Text Analytics suffers f
From playlist Introduction to Text Analytics with R
Computational Linear Algebra 10: QR Algorithm to find Eigenvalues, Implementing QR Decomposition
Course materials available here: https://github.com/fastai/numerical-linear-algebra We discuss the QR algorithm to find eigenvalues, and a few ways to implement the QR factorization. - QR algorithm - Linear algebra projections - Gram-Schmidt - Householder - Stability Examples Course overv
From playlist Computational Linear Algebra
17. Orthogonal Matrices and Gram-Schmidt
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 17. Orthogonal Matrices and Gram-Schmidt License: Creative Commons BY-NC-SA More information a
From playlist MIT 18.06 Linear Algebra, Spring 2005
Lecture 11: Minimizing ‖x‖ Subject to Ax = b
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k In this lecture, P
From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Diagonalizing a symmetric matrix. Orthogonal diagonalization. Finding D and P such that A = PDPT. Finding the spectral decomposition of a matrix. Featuring the Spectral Theorem Check out my Symmetric Matrices playlist: https://www.youtube.com/watch?v=MyziVYheXf8&list=PLJb1qAQIrmmD8boOz9a8
From playlist Symmetric Matrices
Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 29-VMLS mtrx pwrs & QR fac
Professor Stephen Boyd Samsung Professor in the School of Engineering Director of the Information Systems Laboratory To follow along with the course schedule and syllabus, visit: https://web.stanford.edu/class/engr108/ To view all online courses and programs offered by Stanford, visit:
From playlist Stanford ENGR108: Introduction to Applied Linear Algebra —Vectors, Matrices, and Least Squares
VSM, LSA, & SVD | Introduction to Text Analytics with R Part 7
Part 7 of this video series includes specific coverage of: – The trade-offs of expanding the text analytics feature space with n-grams. – How bag-of-words representations map to the vector space model (VSM). – Usage of the dot product between document vectors as a proxy for correlation. –
From playlist Introduction to Text Analytics with R
Gram-Schmidt Process: Find an Orthogonal Basis (3 Vectors in R3)
This video explains how determine an orthogonal basis given a basis for a subspace.
From playlist Orthogonal and Orthonormal Sets of Vectors
This video defines elementary matrices and then provides several examples of determining if a given matrix is an elementary matrix. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Augmented Matrices
Lec 14 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 14: Exam Review License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008