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...
In this paper we characterize the nonnegative nonsingular tridiagonal matrices belonging to the class of inverse M-matrices. 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....
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...
The triangular transformation relationship of the simplified upper limb model is presented in Table2. The triangles can be selected according to the DOFs required to estimate the motion angles and describe the motion of the upper limb, which reflects the generality of the model. If the required D...
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...
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))...
Our results extend to a broader class of “chain structured tropical matrix semigroups”; we exhibit a faithful representation of the free monogenic inverse semigroup within such a semigroup, which leads also to a representation by 3×3 upper triangular tropical matrices....
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...