Adjoint example sentences

"Adjoint" Example Sentences

1. The adjoint operator is an important concept in linear algebra.
2. The linear function has an adjoint map.
3. The matrix representation of the adjoint operator is the conjugate transpose.
4. The adjoint matrix has the same eigenvectors as its corresponding matrix.
5. The adjoint of a linear transformation is unique.
6. A self-adjoint operator is its own adjoint.
7. The adjoint of a complex-valued function is its conjugate.
8. The adjoint of a real-valued function is the same function.
9. The adjoint of a bounded linear operator is also bounded.
10. The adjoint space is the space of all linear functionals on a given vector space.
11. The adjoint of a closed linear operator is always closed.
12. The adjoint of a differential operator is also a differential operator.
13. A normal operator is self-adjoint if and only if its eigenvectors form an orthonormal basis.
14. The adjoint of a matrix can be computed using the formula A* = (adj (A))^T.
15. The adjoint of a reflection is itself.
16. The adjoint of a projection is also a projection.
17. The adjoint of a unitary operator is its inverse.
18. The adjoint of a Hermitian matrix is also Hermitian.
19. The adjoint of a positive definite matrix is also positive definite.
20. The adjoint of a skew-symmetric matrix is also skew-symmetric.
21. There exists a unique adjoint for each linear operator on a given vector space.
22. The adjoint of a normal matrix is also normal.
23. The adjoint of a symplectic operator is also symplectic.
24. The adjoint of a trace class operator is also trace class.
25. The inner product of two vectors is given by the adjoint of the operator applied to one of the vectors.
26. The adjoint of the identity operator is the identity operator.
27. The adjoint of a bilinear form is its transpose.
28. The adjoint of the Laplace operator is itself.
29. The adjoint of a linear functional is a linear operator.
30. The adjoint of a bounded linear transformation satisfies the property (AB)^* = B^* A^*.

Common Phrases

1. Adjoint matrix;
2. Adjoint operator;
3. Adjoint algorithm;
4. Adjoint function;
5. Adjoint system;
6. Adjoint solution;
7. Adjoint sensitivity;
8. Adjoint state;
9. Adjoint boundary conditions;
10. Adjoint gradient.