Vectors and Matrices in Data Mining and Pattern Recognition
... Thus the query itself is considered as a document. The information retrieval task can now be formulated as a mathematical problem: find the columns of A that are close to the vector q. To solve this problem we must use some distance measure in R10 . In the information retrieval application it is comm ...
... Thus the query itself is considered as a document. The information retrieval task can now be formulated as a mathematical problem: find the columns of A that are close to the vector q. To solve this problem we must use some distance measure in R10 . In the information retrieval application it is comm ...
Rotation matrices - CS HUJI Home Page
... transforms ~0 = (0, 0) to a point other than ~0 = (0, 0). However, if we want to rotate around an arbitrary rotation center c, we can shift the plane by −c such that the rotation center will be 0, then perform the rotation around (0, 0) and shift the plane back by +c: Rc,α (x) = Rα (x − c) + c = Rα ...
... transforms ~0 = (0, 0) to a point other than ~0 = (0, 0). However, if we want to rotate around an arbitrary rotation center c, we can shift the plane by −c such that the rotation center will be 0, then perform the rotation around (0, 0) and shift the plane back by +c: Rc,α (x) = Rα (x − c) + c = Rα ...
a ,b
... (0,1,0), and (0,0,1) under the rotation. Turn in the source code, the rotation quaternion, and the images. 3. Use the quaternion multiplication package in Mathematica to perform the same rotation described in 2. Turn in the Mathematica notebook. It should include the rotation quaternion used, the im ...
... (0,1,0), and (0,0,1) under the rotation. Turn in the source code, the rotation quaternion, and the images. 3. Use the quaternion multiplication package in Mathematica to perform the same rotation described in 2. Turn in the Mathematica notebook. It should include the rotation quaternion used, the im ...
Matlab Tutorial I
... The former is accomplished with the * operator, just as if you were multiplying two scalars together. The latter is accomplished with the .* operator (a period before the asterisk). So [1 2 3] .* [4 5 6] = [4 10 18] but [1 2 3] * [4 5 6]’ = 32 (note the transpose operator) and [1 2 3] * [4 5 6] is ...
... The former is accomplished with the * operator, just as if you were multiplying two scalars together. The latter is accomplished with the .* operator (a period before the asterisk). So [1 2 3] .* [4 5 6] = [4 10 18] but [1 2 3] * [4 5 6]’ = 32 (note the transpose operator) and [1 2 3] * [4 5 6] is ...
Rotations in higher dimensions
... One day in section, Kristen asked the interesting question of what a ”rotation” in R10 looks like. This is beyond the course, you’ll never be asked to apply geometric concepts to high dimensions, but if you wonder where all our definitions come from, or want a glimpse into how research mathematician ...
... One day in section, Kristen asked the interesting question of what a ”rotation” in R10 looks like. This is beyond the course, you’ll never be asked to apply geometric concepts to high dimensions, but if you wonder where all our definitions come from, or want a glimpse into how research mathematician ...
Vector coordinates, matrix elements and changes of basis
... In particular, suppose B = Bs is the standard basis. Then to change from Bs to C is geometrically equivalent to starting with a definition of the x, y and z axis, and then defining a new set of axes. Note that we have not yet introduced the concept of an inner product or norm, so there is no concept ...
... In particular, suppose B = Bs is the standard basis. Then to change from Bs to C is geometrically equivalent to starting with a definition of the x, y and z axis, and then defining a new set of axes. Note that we have not yet introduced the concept of an inner product or norm, so there is no concept ...
FAMILIES OF SIMPLE GROUPS Today we showed that the groups
... but finitely many of the other finite simple groups also fall into infinite families, and these families generally consist of invertible matrices over finite fields such as Fp (the integers mod p, p a prime). Later in the course we will learn that there is a finite field Fq of order q = pr , r ∈ N+ ...
... but finitely many of the other finite simple groups also fall into infinite families, and these families generally consist of invertible matrices over finite fields such as Fp (the integers mod p, p a prime). Later in the course we will learn that there is a finite field Fq of order q = pr , r ∈ N+ ...
The matrix of a linear operator in a pair of ordered bases∗
... Example 1. Let us give some examples of a linear operator A : V → W : a) V = W = R2 , A(x1 , x2 ) = (x1 , −x2 ) (reflection of a plane in the x1 - axis); b) V = W = R2 , A(x1 , x2 ) = (−x1 , −x2 ) (symmetry of a plane about the origin); c) V = W = R2 , A(x1 , x2 ) = (x1 , 0) (orthogonal projection o ...
... Example 1. Let us give some examples of a linear operator A : V → W : a) V = W = R2 , A(x1 , x2 ) = (x1 , −x2 ) (reflection of a plane in the x1 - axis); b) V = W = R2 , A(x1 , x2 ) = (−x1 , −x2 ) (symmetry of a plane about the origin); c) V = W = R2 , A(x1 , x2 ) = (x1 , 0) (orthogonal projection o ...
Lecture 1
... KEY WORDS. Matrix, vector, transpose, inverse, determinant, linear system of equations. GOAL. Be able to perform the basic matrix operation, such as transpose, inverse, product, determinant etc; be able to represent a linear system of equations in a matrix vector form. ...
... KEY WORDS. Matrix, vector, transpose, inverse, determinant, linear system of equations. GOAL. Be able to perform the basic matrix operation, such as transpose, inverse, product, determinant etc; be able to represent a linear system of equations in a matrix vector form. ...
The Elimination Method for solving large systems of linear
... For a given non-singular matrix A, the inverse matrix B A1 exists such that AB BA I , where I is an identity matrix of order same as A or B. A matrix A is non-singular iff det( A) | A | 0 To find inverse of a nonsingular matrix using calculator: Step 1. Input the matrix say A Step 2. Call m ...
... For a given non-singular matrix A, the inverse matrix B A1 exists such that AB BA I , where I is an identity matrix of order same as A or B. A matrix A is non-singular iff det( A) | A | 0 To find inverse of a nonsingular matrix using calculator: Step 1. Input the matrix say A Step 2. Call m ...
Square Roots of 2x2 Matrices - Digital Commons @ SUNY Plattsburgh
... We shall now prove Theorem 1 in two ways; the first utilizing the fact that the roots of p(x) are slopes of eigenvectors, the second related to the system of differential equations defined by A. We assume that p(x) has distinct real roots (which, since the discriminant of p(x) is the same as that of ...
... We shall now prove Theorem 1 in two ways; the first utilizing the fact that the roots of p(x) are slopes of eigenvectors, the second related to the system of differential equations defined by A. We assume that p(x) has distinct real roots (which, since the discriminant of p(x) is the same as that of ...
