Sentence examples for matrix with determinant from inspiring English sources

For an orthogonal matrix with determinant 1, we define (1.11).

A unitary matrix with determinant equal to one can be constructed as the product of elementary unitary matrices with determinant equal to one [13].

A special orthogonal matrix is an orthogonal matrix with determinant +1.

As a linear transformation, every orthogonal matrix with determinant +1 is a pure rotation, while every orthogonal matrix with determinant -1 is either a pure reflection, or a composition of reflection and rotation.

We construct unitary matrices with determinant one as a product of 1 2 N ( N − 1 ) elementary N-dimensional unitary matrices A = ∏ i = 1 N ∏ j = i + 1 N T ij.

Let Cp + q be equipped with a hermitian form of signature (p, q) and let SU p, q) denote the subgroup of the corresponding invariance group U p,q) consisting of matrices with determinant 1.

The direct isometries (preserving the orientation) in D are the elements of the special unitary group, noted SU ( 1, 1 ), of 2 × 2 Hermitian matrices with determinant equal to 1. Given: γ = such that | α | 2 − | β | 2 = 1, an element of SU ( 1, 1 ), the corresponding isometry γ in D is defined by: γ ⋅ z = α z + β β ¯ z + α ¯, z ∈ D. (32).

Orthogonal matrices with determinant 1 form a subgroup called special orthogonal group.

In other words, the elements of which conjugate with are matrices with determinant equal to −1.

The rotation matrix Q is an orthogonal matrix with a determinant one, which lies exactly on the manifold of the special orthogonal group begin{array}{*{20}l} SO(3) = left{ mathbf{Q} in mathbb{R}^{3 times 3}: mathbf{Q}^{top} mathbf{Q} = mathbf{I}, det(mathbf{Q}) = 1right}.

where denotes the group of orthogonal matrices on with determinants 1.