与 «ORTHOGONAL MATRIX»相关的英语书籍
在以下的参考文献中发现
orthogonal matrix的用法。与
orthogonal matrix相关的书籍以及同一来源的简短摘要提供其在 英语文献中的使用情境。
1
Matrices and Tensors in Physics
which is a unit matrix, showing that A is an orthogonal matrix. Now since for an
orthogonal matrix, its inverse is equal to its transpose, A"1 is given by Eq. (33). I
The elements of an orthogonal matrix may be real or complex. For example ...
2
Matrices and Transformations
Similarly, it follows that the column vectors of an orthogonal matrix A are mutually
orthogonal unit vectors since AT A = 1. 1f A is an orthogonal matrix, 04-%4'l)r =
XrMOr = ATA — /; that is, the inverse (transpose) of an orthogonal matrix is an ...
Anthony J. Pettofrezzo, 1978
3
Matrix Theory: Basic Results and Techniques
We show that a real orthogonal matrix is similar to a direct sum of real orthogonal
matrices of order 1 or 2. Theorem 6.4 Every real orthogonal matrix is real
orthogonally similar to a direct sum of real orthogonal matrices of order at most 2.
Proof.
4
Engineering Mathematics - I
2.4 Orthogonal Transformation and Orthogonal Matrix If matrix A is orthogonal
then A T = A _1 . Multiplying both sides by A, we get A'A = A-1 A (v A_1A = i) i.e. I
- A'A Pre-multiplying by X' and post-multiplying by X where X is a column vector
of ...
(b) Show that the complex eigenvalues, if any, of an orthogonal matrix occur in
conjugate pairs. (c) Show that all eigenvalues of a unitary (and hence, in
particular, of an orthogonal) matrix have unit modulus. Solution (a) Consider the
example ...
Karim M. Abadir, Jan R. Magnus, 2005
6
Convex Optimization & Euclidean Distance Geometry
The property Q−1 = QT completely defines an orthogonal matrix Q∈Rn×n
employed to effect vector rotation; [292, 2.6, 3.4] [294, 6.5] [180, 2.1] for any x∈
Rn Qx = x (1545) A unitary matrix is a complex generalization of the orthogonal
matrix.
... and hence dim(nullspace(A)) : 0 (0.2.3.1). Compute A(AB — BA): A(I — BA): A
— (AB)A : A—A:0,soAB—BA:0. 2.1.P8 A matrix A G M, is complex orthogonal if
ATA : I. (a) Show that a complex orthogonal matrix is unitary if and only if it is real.
Roger A. Horn, Charles R. Johnson, 2012
8
Elementary
Matrix Theory
This outstanding text offers an unusual introduction to matrix theory at the undergraduate level.
9
Matrix theory and applications
The matrix Q is the desired orthogonal matrix. Other methods use the relation
between an orthogonal matrix and skew- symmetrix matrix or Householder
transformation. These methods are discussed in Anderson, Olkin and Underhill (
1987).
10
Matrix Algebra From a Statistician's Perspective
Definition and basic properties and results A (square) matrix A is said to be an
orthogonal matrix if A0A D AA0 D I or, equivalently, if A is nonsingular and A1 D
A0. To show that a (square) matrix A is orthogonal, it suffices (in light of Lemma ...
包含词语«ORTHOGONAL MATRIX»的新条目
找出国内和国际出版社所讨论的内容，以及词语
orthogonal matrix在以下新条目的上下文中是如何使用的。
how to get unit vector perpendicular to normal surface
Return an orthogonal matrix defining a basis for the coordinate frame of a plane with the specified normal. /** * The normal becomes the ... «GameDev.net, 三月 15»
Directional light position in shadow mapping
You don't calculate a position, you calculate an orthogonal matrix. ... Build an orthogonal matrix based on the list of objects you just created. «GameDev.net, 三月 15»
Terrain sculpting
The vertex shader could use a screen quad and an orthogonal matrix projection to position the rendering such that you update only the part of ... «GameDev.net, 一月 15»
Frustum Planes, have to transpose view matrix first?
to explain more, orthogonal matrix transpose is its inverse, but if this transposed matrix is considered in reverse majoring (column to row or ... «GameDev.net, 六月 14»
Unity-like transform component
A child object that has a non-uniformly scaled parent and is rotated relative to that parent may have a non-orthogonal matrix, meaning that it ... «GameDev.net, 二月 14»
DirectX 11 C++ Game Camera
One is called orthogonal matrix and other is called perspective matrix. Orthogonal matrix serves for projecting 3D point into 2D without saving ... «GameDev.net, 三月 13»
What Is The Geometry Of Spacetime? — What Kinds Of Inner …
For instance, if we follow the orthogonal matrix that diagonalizes our symmetric matrix, g, by a diagonal matrix, d, we can rescale the diagonal ... «Science 2.0, 十一月 12»
The OpenACC Execution Model
... that can be termed triangular orthogonalization, meaning a set of triangular matrices are applied on a matrix to produce an orthogonal matrix. «Dr. Dobb's, 八月 12»
New masterplanned capital for African nation
Envisaged as the president's dream city, 'Djibloho' uses an orthogonal matrix that takes advantage of the existing road network to connect ... «Construction Week Online, 十一月 11»
Orthogonal matrix issue
With a orthogonal matrix, nothing renders at all. I'm using my own projection matrix functions to generate the matrices, so naturally, my first ... «GameDev.net, 八月 11»
