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Dual-Manipulator Testing Technique
Published in Chunguang Xu, Robotic Nondestructive Testing Technology, 2022
According to the theories of Lie group and Lie algebra, the exponential matrix of a skew symmetric matrix is an orthogonal matrix. In the inverse function, the logarithm matrix of an orthogonal matrix is a skew symmetric matrix. Skew symmetric matrix is a square matrix whose transpose plus itself is equal to null matrix. In the real number domain, a skew symmetric matrix represents an identity matrix mapped from the tangent space to the real orthogonal group O(n). This is the so-called special orthogonal Lie algebra. Therefore, skew symmetric matrix can be regarded as an infinitesimal rotation, and its space constitutes the Lie algebra O(n) of the Lie group O(n). It is easy to prove that the addition and subtraction of two skew symmetric matrices will still produce a skew symmetric matrix.
Matrix Algebra
Published in Rowan Garnier, John Taylor, Discrete Mathematics, 2020
A square matrix is one having the same number of rows as it has columns. The following are examples of square matrices: (23-14)(32045-12-37).
Matrices
Published in C.W. Evans, Engineering Mathematics, 2019
A square matrix M is symmetric if and only if it is equal to its transpose. Obtain a, b and c if A=[3a−125cb82]
Application of Tikhonov regularization to reconstruct past climate record from borehole temperature
Published in Inverse Problems in Science and Engineering, 2021
Jia Liu, Tingjun Zhang, Gary D. Clow, Elchin Jafarov
The Generalized Cross-Validation (GCV) method employs the GCV function to find a regularization parameter α. The optimal regularization parameter α is the one that minimizes the GCV function: where is a matrix that generates the regularized solution when multiplied by d, i.e.. Here, In is the identity matrix of dimension n×n. trace(·) is a mathematical operator on a square matrix, defined to be the sum of the elements on the matrix diagonal.
Development of a novel integrated value engineering and risk assessment (VENRA) framework for shipyard performance measurement: a case study for an Indonesian shipyard
Published in Ships and Offshore Structures, 2023
Imam Baihaqi, Iraklis Lazakis, Rafet Emek Kurt
Step 4: Obtain the fuzzy total-relation matrix using equations (4) to (7). where, and I is the identity matrix. Identity matrix I is square matrix with ones on the main diagonal and zeros elsewhere.