Descriptive Statistics
... This is the unbiased formula for S. From time to time we might have occasion to see the maximum likelihood formula which uses n instead of n - 1. The covariance matrix is a symmetric matrix, square, with as many rows (and columns) as there are variables. We can think of it as summarizing the relatio ...
... This is the unbiased formula for S. From time to time we might have occasion to see the maximum likelihood formula which uses n instead of n - 1. The covariance matrix is a symmetric matrix, square, with as many rows (and columns) as there are variables. We can think of it as summarizing the relatio ...
Review of Linear Algebra
... m rows and n columns. We refer to the number aij as the ij th entry. This means that aij is the number in the ith row and j th column. In particular a vector (x1 , . . . , xn ) is also a matrix, in this case a 1 × n matrix. We will call such a matrix a row vector. We can also think of a vector as an ...
... m rows and n columns. We refer to the number aij as the ij th entry. This means that aij is the number in the ith row and j th column. In particular a vector (x1 , . . . , xn ) is also a matrix, in this case a 1 × n matrix. We will call such a matrix a row vector. We can also think of a vector as an ...
LINEAR ALGEBRA (1) True or False? (No explanation required
... Explanations: matrices like ( 10 00 ) or ( 11 11 ) are nonzero but do not have an inverse. Matrices have an inverse if and only if they are nonsingular square matrices. If A and B are nonsingular, then so is AB, and its inverse clearly is B −1 A−1 since B −1 A−1 AB = B −1 IB = B −1 B = I. In general ...
... Explanations: matrices like ( 10 00 ) or ( 11 11 ) are nonzero but do not have an inverse. Matrices have an inverse if and only if they are nonsingular square matrices. If A and B are nonsingular, then so is AB, and its inverse clearly is B −1 A−1 since B −1 A−1 AB = B −1 IB = B −1 B = I. In general ...
Notes
... (solving a linear system). Ill-conditioned matrices are “close to” singular in a well-defined sense: if κ(A) 1, then there is a perturbation E, kEk kAk, such that A + E is singular. An exactly singular matrix (which has no inverse) can be thought of as infinitely ill-conditioned. That is because ...
... (solving a linear system). Ill-conditioned matrices are “close to” singular in a well-defined sense: if κ(A) 1, then there is a perturbation E, kEk kAk, such that A + E is singular. An exactly singular matrix (which has no inverse) can be thought of as infinitely ill-conditioned. That is because ...
More Possible Mathematical Models
... can explain why matrix multiplication for square matrices is not commutative but is associative and distributive. I can explain the role of a zero matrix and identity matrix in matrix addition and multiplication and how each is similar to the role of one in the real ...
... can explain why matrix multiplication for square matrices is not commutative but is associative and distributive. I can explain the role of a zero matrix and identity matrix in matrix addition and multiplication and how each is similar to the role of one in the real ...
Test_1_Matrices_AssignSheet
... Notes Add, Subtract, Add, Subtract matrices of appropriate dimensions. Multiply matrices by a scalar to produce a new matrix. multiply by scalar Instruction: Discussion & Group Practice Classwork: Differentiation: Individual pacing/questions WS 1.1 #1-10 Homework: WS 1.1a #1-14 Day 2 ...
... Notes Add, Subtract, Add, Subtract matrices of appropriate dimensions. Multiply matrices by a scalar to produce a new matrix. multiply by scalar Instruction: Discussion & Group Practice Classwork: Differentiation: Individual pacing/questions WS 1.1 #1-10 Homework: WS 1.1a #1-14 Day 2 ...
Linear Systems
... • Linear Systems are found in every habitat: – simple algebra – solutions to ODEs & PDEs – statistics (especially, least squares) ...
... • Linear Systems are found in every habitat: – simple algebra – solutions to ODEs & PDEs – statistics (especially, least squares) ...
Matrix: TI-89
... Create a Matrix to use in a Test of Independence on the TI-89 Press APPS 6:Data/Matrix Editor Press 3:New Aroow over and down to 2:Matrix. Press Enter Arrow down to Folder. Either use the one that is there or arrow over and down to another folder name (don't use statvars) and press Enter. Arrow down ...
... Create a Matrix to use in a Test of Independence on the TI-89 Press APPS 6:Data/Matrix Editor Press 3:New Aroow over and down to 2:Matrix. Press Enter Arrow down to Folder. Either use the one that is there or arrow over and down to another folder name (don't use statvars) and press Enter. Arrow down ...
We can treat this iteratively, starting at x0, and finding xi+1 = xi . This
... The Range, range(A), or span of an m ⇥ n matrix A is the set of vectors y 2 Rm such that y = Ax for some x 2 Rn . The range is also referred to as the column space of A as it is the space of all linear combinations of the columns of A. The Nullspace, null(A), of an m ⇥ n matrix A is the set of vecto ...
... The Range, range(A), or span of an m ⇥ n matrix A is the set of vectors y 2 Rm such that y = Ax for some x 2 Rn . The range is also referred to as the column space of A as it is the space of all linear combinations of the columns of A. The Nullspace, null(A), of an m ⇥ n matrix A is the set of vecto ...
Linear Algebra Homework 5 Instructions: You can either print out the
... or other ways that clearly shows your work and computations. Write your UNI in the right top corner of each page. and your name in the left top corner. For computational excercise, circle the final answer. This homework is due at 4:30pm June, 15th. Problem 1. Read the notes Page 68 to Page 71 about ...
... or other ways that clearly shows your work and computations. Write your UNI in the right top corner of each page. and your name in the left top corner. For computational excercise, circle the final answer. This homework is due at 4:30pm June, 15th. Problem 1. Read the notes Page 68 to Page 71 about ...
Non-negative matrix factorization
NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.