We give a geometric equivalence for a nonnegative nonsingular upper triangular matrix to be in this class. This equivalence is extended to include some reducible matrices.I.N.ImamSDOSLinear Algebra & Its ApplicationsI.N. Imam, Tridiagonal and upper triangular inverse M-matrices, Linear Algebra ...
The inverse of unit upper (unit lower) triangular matrix is unit upper (unit lower) triangular. • The product of two upper (lower) triangular matrices is upper (lower) triangular matrix. • The product of two unit upper (unit lower) triangular matrices is unit upper (unit lower) triang...
Inverse-preserving linear operators on spaces of upper triangular matrices over commutative integral domain 交换整环上三角矩阵的保逆线性算子 service.ilib.cn 6. Automorphisms of the Upper Triangular Matrix Ring over Commutative Rings 交换环上上三角矩阵环的自同构 www.ilib.cn 7. Automorphisms of the Str...
We will need the following classical bounds for the norm of the inverse matrices which is due to Richter [25] (see also [18] for a different proof). Recall that for a matrix A, \(\Vert A\Vert \) stands for the operator norm \(\ell ^2\rightarrow \ell ^2.\) Theorem...
The upper quasi-triangular matrix T, in Schur canonical form. LDT (input) The leading dimension of the array T. LDT > = max(1,N). VL (input) If JOB = 'E' or 'B', VL must contain left eigenvectors of T (or of any Q*T*Q**T with Q orthogonal), corresponding to the eigenpair...
(TPS), maps the problem in Euclidean space to TPS, is utilized for inverse solving of 1–8 DOFs of the upper limb, and provides a mathematical description of upper-limb motions. The results largely satisfied realistic motion of the upper limbs. The coordinate information of a maximum of six...
Here,τcdenotes the torque applied to the robot joints. The termsB(q)andn(q,q˙)account for inertial properties and dynamic effects including Coriolis and gravitational forces.JA†(q)is the pseudo-inverse matrix of the analytical Jacobian. Additionally,x~randx~tindicate the radial and tangent...
Examples of specific tool types: 1, asymmetrical bifacial-backed knife (Keilmesser); 2, convergent flake with proximal inverse kombewa removals; 3, bifacial preform Full size image Another small bifacial piece displays an advanced stage of thinning, but marginal retouch is absent (Fig.21(3))...
Construction of fuzzy pair-wise comparison matrix The first task of the fuzzy AHP method is to decide on the relative importance of each pair of factors in the same hierarchy (Chang 1996). The triangular fuzzy number used for pair-wise comparison matrix, the fuzzy evolution matrix (\(\tilde...
8.The authors characterize the forms of additive invertable operators preserving inverse matrix of the upper triangular matrix space over a field which characteristic is not 2 or 3 .刻划了特征不为2及3的域上的上三角矩阵空间保逆矩阵的可逆加法算子的形式。