dragonbox algebra

This section mainly reviews some simple knowledge about linear algebra.Matrix and vector Matrix Number of $ m \ times N $ A _ {IJ} (I = ,..., m; j = 1, 2 ,..., n) $ the number table of $ M $ row $ N $ column, which is called the matrix of $ M $ row $

This time, the core content is entered, and feature values and feature vectors are calculated. I believe that with the foundation of the first two articles, you will not feel any obstacles. Enter the subject 1. Calculate the feature value For the

Exercise: 7. rewrite theorem 1.4.10 to a more general language. The first sentence is: "set $ F $ to the full homomorphic of the group $ g _ {1} $ to $ g _ {2} $, and $ H Similar to this theorem, we provide the following solutions: (1) $ HN $ is

1. Linear Combination For n-dimensional vector groups {V1, V2, V3 ,..., VK}, if any real number C1, C2, C3 ,... CK, then the vector V' = C1 * V1 + C2 * V2 +... + ck * VK is a linear combination of vector groups. a linear combination refers to a

In the previous article, we have defined the transpose matrix. The transpose matrix of A is recorded as T (A), and we know that det (A) = det (A transpose ). 1. Transpose of Matrix ProductMatrix A and B, with T (AB) = T (B) * t ().Matrix A1, a2...

Original: Click to open the link "Homogeneous coordinate representation" is one of the important means of computer graphics, it can be used to distinguish between vectors and points, and it is more easily used for affine (linear) geometric

AI indicates whether each node is a button, according to the case of each point equation Total n unknowns, n equations After the Gauss elimination, may appear the free element, the 2^s enumeration free element Choice, calculates the

section Fourth two and its standard form A. Mathematical Concepts 1. Two-time type A two-time homogeneous function called n variables is a two-time type. 2. Matrix form of two-times type 3. Rank of two-time type The rank =r of f (a). 4.

1 ($ 15' $) The first coefficient with the lowest number of results is $1 $ real number polynomial $ f (x) $ \ Bex F (0) = 7, \ quad F (1) = 14, \ quad F (2) = 35, \ quad F (3) = 76. \ EEx $ Answer: Set $ f (x) = x ^ 4 + a_3x ^ 3 + a_2x ^ 2 + a_1x +

1 ($ 15' $) set $ \ BBP $ to a number field, $ f (x), g (x) \ In \ BBP [x] $, and $ \ P (g (x) \ geq 1 $. proof: There is a unique polynomial sequence $ f_0 (x), F_1 (x), \ cdots, f_r (x) $, make $ \ P (f_ I (x) Proof: by division with remainder, $

Exercise: 4. It is proved that the subgroups with an exponent of $2 $ must be regular. It is proved that if $ G $ is set as a group and $ H is $ G = H \ cup ah, A \ notin h $ There must be right companion set decomposition. $ G = H \ cup ha

1. Vector point Multiplication The result of dot multiplication between vector A and vector B is a scalar defined as a. B = A1 * B1 +... + an * bn. 2. Vector LengthThe length of vector V is also a scalar, defined as | v | = SQRT (V1 * V1 + V2 * V2 +.

1. Inverse TransformationConstant transformation, defined as IX: Rn-> RM, in (x) = x; equivalent to transformation from itself to itself;Define the inverse conversion, and convert FX: Rn-> RM. If f'y: Rm-> RN, f' of = in and fof' = IM, f' is called

Algebraic operations for digital image processing: (1) Addition operation: Clear A=imread('test.jpg '); S = size (); B = double (); P = size (B) C (:,:, 1) = B (:,:, 1) + B (:,:, 2); % Add the red component C (:,:, 2) = B (:,:, 2 ); C (:,:, 3) =

Common LINALG functions function Description Diag Returns the diagonal (or non-diagonal) elements of a matrix in the form of a one-dimensional array, or converts a one-dimensional array to a matrix

The trace of a matrix is the sum of the diagonal elements of a matrix. Has the following properties: TR (AB) =tr (BA) ∂TR (AB) ∂A=BT Based on the above two properties can basically do the next operation. First, the following derivatives

involves abstract representative Mathematics (including group theory, ring and algebra theory, domain theory, lattice theory, overall Li Qun theory, algebra group theory, simultaneous modulation algebra and various derivative structure theories) general topology, Point Set Topology, measurement and integral theory, and functional analysis (including linear topol

curves were what people could see in space. the high dimension has a little fictional component, which people can imagine through mathematical thinking, but at that time people may not take them seriously. take them seriously and study them with the same degree of attentionThis idea is actually a product of the 20th century. similarly, there is no clear evidence that our pioneers in the 19th century have considered the increase in the number of functions. The research is not just a single but a

-Taki-"One ball can be divided into five parts, after performing a series of rigid transformations (translation rotation) on them, they can be combined into twoSame size". It is precisely because of these conclusions that are totally against common sense that the mathematics field once had a heated debate over whether to accept it for a long time. Now, mainstream mathematicians should basically accept it, because many important theorems of mathematical branches depend on it. In the subjects we w

debate over whether to accept it for a long time. Now, mainstream mathematicians should basically accept it, because many important theorems of mathematical branches depend on it. In the subjects we will discuss later, the following theorem relies on the choice principle: Topology: Baire Category Theorem Real analysis (measure theory): the existence of the unmeasurable set of Lebesgue Four major theorems of functional analysis: Hahn-Banach Extension Theorem, Banach-Steinhaus Theorem (Unifor