matrices precalculus

2016-01-27 21:03 524 People read comments (0) favorite reports Classification:theory/Notes (a) Copyright NOTICE: This article for Bo Master original article, reproduced please indicate the source, thank you!Title: symmetric matrix, Hermite matrix, orthogonal matrix, unitary matrix, singular matrix, normal matrix, idempotent matrixLook at the literature, often see a variety of matrices, this chapter summarizes the common symmetry matrix, Hermite mat

The elementary transformation of the Matrix one. Mathematical concepts The nature of an equivalence relationship: (i) reflexive a~a; (ii) If the symmetry of  is a~b, then b~a; (iii) If the transitivity is A~b, the b~c is a~c; Two. focus, difficulty analysis The focus of this section is to use matrix Elementary transformations to transform matrices into row (column) ladder-shaped matrices, minimalist

I_dovelemonSource: CSDNDate: 2015/5/18Topics: affine transformations, orthogonal matrices, inversion, matrix multiplicationIntroductionLong time no blog, this period has been busy, today to write down the internship when the problems encountered, while continuing to update their blog.What I want to say today is some of the doubts about the 3D transformation. Mainly in what is affine transformation? What is an orthogonal matrix? How to find out the inv

Transferred from: http://www.cnblogs.com/soroman/archive/2008/03/21/1115571.htmlThinking: Matrices and transformations, and the use of matrices in DirectX and OpenGL1. Matrix and Linear transformations: one by one correspondenceA matrix is a tool used to represent a linear transformation, which corresponds to a linear transformation of one by one.Consider a linear transformation:a11*x1 + a12*x2 + ... +a1n*x

Set a n*n square a,a any element a[i][j], when and only if a[i][j] = = A[j][i](0 0 650) this.width=650; "src=" Http://s1.51cto.com/wyfs02/M01/7E/ED/wKiom1cMz5zzQr_rAAAb3l_RgBs093.png "title=" QQ picture 20160412183656.png "alt=" Wkiom1cmz5zzqr_raaab3l_rgbs093.png "/>For example, symmetric matrix compression storage storage only need to store the upper triangle/lower triangle of data, under normal circumstances with the lower triangle storage, so up to N (n+1)/2 data.The correspondence between

Set a n*n square a,a any element a[i][j], when and only if a[i][j] = = A[j][i] (0 0 N-1), then matrix A is a symmetric matrix.Separated by the diagonal of the matrix, it is divided into upper and lower triangles.For example, symmetric matrix compression storage storage only needs to store the upper triangle/lower triangle of data, under normal circumstances, with the lower triangle storage, so the maximum storage n (n+1)/2 data.The correspondence between symmetric

Rotate and print order n matrices clockwise (0th questions) and matrices 4thQuestion requirements Problem description: clockwise rotation of the n-order matrix Example input: 4 1 2 3 4 12 13 14 5 11 16 15 6 10 9 8 7 Sample output: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Solution First, establishPrint in circlesFirst print the outermost circle, then print the circle in the middle, and so on. During printing, t

What is a symmetric matrix (Symmetricmatrix)?Symmetrical symmetry-------SeeSet a n*n square a,a any element Aij, when and only if Aij = = Aji(0 Compressed storage is the matrix storage only need to store the upper triangle/lower triangle of data, so the maximum number of N (n+1)/2 data.the correspondence between symmetric matrices and compressed storage: Lower triangle storage i>=j, S YMMETRICM Atrix [i][j] = = array[i* (i+1)/2+j]650) this.width=6

Set a n*n square a,a any element Aij, when and only if Aij = = Aji(0 Compressed storage is called a matrix storage only need to store the upper triangle/lower triangle of data, so the maximum storage N (n+1)/2 data.symmetric matrix and compressed storage correspondence: Lower triangle storage i>=j, Symmetricmatrix[i][j] = = array[i* (i+1)/2+j]650) this.width=650; "src="/e/u261/themes/default/images/spacer.gif "style=" Background:url ("/e/u261/lang/zh-cn/ Images/localimage.png ") no-repeat cente

" Let's view these points in a (pseudo) three dimensional scatterplot:So let ' s follow the steps listed above. (1) The origin of the new coordinate system would be located at(1.5,1.5,1.5) . (2) The axes is already equal. (3) The first principal component would go diagonally from(0,0,0) To(3,3,3) , which is the direction of greatest variation for these data. Now, the second principal component must is orthogonal to the first, and should go in the direction of the gre

scare peopleFigure 1:A c e is multiplied by X y 1 and summed to produce the result x ' = ax + cy + E;b d f and X y 1 are multiplied and summed to produce the result y ' = bx + dy + F;The x y is the center point before the element transformation, that is, the value of Transform-origin, and X ' Y ' is the Transform-origin value after the element transformation.Assuming that the center point of an element is 100,100, the element is shifted to the right by 200px, and the center point coordinates ar

The calculation of gradient vectors in deep learning, Jacobian matrices and Hessian matrices are fundamental knowledge points. In fact, the derivative is the linear transformation between linear space, and the Jaocibian matrix is the derivative in essence. For example, the derivative of the map is the linear mapping between the tangent space at the place and the tangent space at the place. The tangent space

satisfies the following properties: (i) nonnegative when x≠0, when x = 0 o'clock,. (ii) homogeneity; (iii) triangular inequalities. 3. is the unit vector. 4. The orthogonal vector group is linearly independent. 5. Schmidt Standard Orthogonal Set linearly independent, Take, make ............................................................ Three. Analysis of key points and difficulties This section mainly describes some preparatory knowledge, its focus is the vector of the inner product, norms

strictly and precisely controlled, and the results are combined (mainly adding) to obtain the final computation result C. Disadvantages 1. Block Size is difficult for different matrix scales, and the block size is limited by the memory size. 2. Block-to-block calculation and organization are cumbersome. 3. It is not conducive to sparse matrix operations (the value 0 occupies a large amount of storage space and does a lot of invalid operations) Algorithm Based on Minimum granularity Multipl

representation of an object with N Independent properties (dimensions), and what is a matrix? If we think that the matrix is an expansion of a new composite vector consisting of a set of column (row) vectors, why is this kind of expansion so widely used? In particular, why is the two-dimensional expansion so useful? If each element in the matrix is a vector, is it more useful if we expand it again and become a three-dimensional square?* Why is the multiplication rule of

unclear. For example:* What exactly is a matrix? Vectors can be thought of as having n mutually independent properties (dimensions)What is the representation of the object and the matrix? If we think that the matrix is a set of columns (rows) of the vector composed of a newThe expansion of the composite vectors, then why this kind of expansion has such a wide range of applications? In particular, toWhat is the two-dimensional expansion so useful? If each element in the matrix is another vector,

definition of a sparse matrix Matrix is now a lot of scientific and engineering computing problems commonly used in the mathematical object, the matrix involved in the calculation of the matrix is usually a higher order than the number of 0 elements is relatively few cases, therefore, we need a way to compress this relatively sparse matrix. The first question, then, is how to define whether a matrix is sparse. Refer to the data structure textbook of Min, page 96th gives the definition of sparse

relationship between eigenvalues of matrices and determinant and trace From:http://www.cnblogs.com/andyjee/p/3737592.htmlThe product of eigenvalues of matrices equals the determinant of matrices The sum of the eigenvalues of the matrices equals the traces of the matrices

Title Description The following definitions are given: Sub-matrices: A new matrix that selects the intersection of some rows and some columns from a matrix (preserving the relative order of rows and columns) is called a sub-matrix of the original matrix. For example, the left-hand image below selects the intersection of the 2nd, 4, and 2nd, 4, and 5 columns to get a 2*3 sub-matrix as shown in the image on the right. 9 3 3) 3 9 9 4 8) 7 4 1 7 4) 6 6

a representation of an object with N Independent properties (dimensions), and what is a matrix? If we think that the matrix is an expansion of a new composite vector consisting of a set of column (row) vectors, why is this kind of expansion so widely used? In particular, why is the two-dimensional expansion so useful? If each element in the matrix is a vector, is it more useful if we expand it again and become a three-dimensional square? * Why is the multiplication rule of