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orthogonal matrix sentence in Hindi

"orthogonal matrix" meaning in Hindiorthogonal matrix in a sentence
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  • The finite-dimensional spectral theorem says that any symmetric matrix whose entries are diagonalized by an orthogonal matrix.
  • An orthogonal matrix " A " is necessarily reflection, or a composition of reflection and rotation.
  • An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of  " 1.
  • The problem of finding the orthogonal matrix Q nearest a given matrix M is related to the Orthogonal Procrustes problem.
  • Dividing " H " through by this length gives an orthogonal matrix whose transpose is thus its inverse.
  • Any orthogonal matrix of size can be constructed as a product of at most " n " such reflections.
  • But surely by my argument, an orthogonal matrix cannot have an eigenvalue that isn't plus or minus one?
  • Where " A " is a 2? orthogonal matrix and is an arbitrary ordered pair of numbers; that is,
  • In Lie group terms, this means that the Lie algebra of an orthogonal matrix group consists of skew-symmetric matrices.
  • As another example, with appropriate normalization the discrete cosine transform ( used in MP3 compression ) is represented by an orthogonal matrix.
  • Conversely, let " Q " be any orthogonal matrix which does not have  " 1 as an eigenvalue; then
  • Going the other direction, the matrix exponential of any skew-symmetric matrix is an orthogonal matrix ( in fact, special orthogonal ).
  • The matrix is a member of the three-dimensional special orthogonal group,, that is it is an orthogonal matrix with determinant 1.
  • In finite-dimensional spaces, the matrix representation ( with respect to an orthonormal basis ) of an orthogonal transformation is an orthogonal matrix.
  • Their cross product is used as the third column in the linear system of equations obtaining a proper orthogonal matrix for the spacecraft attitude given by
  • The representation of a rotation as a quaternion ( 4 numbers ) is more compact than the representation as an orthogonal matrix ( 9 numbers ).
  • A related problem in linear algebra is the "'orthogonal Procrustes problem "'of finding the closest orthogonal matrix to any given matrix.
  • Generalizing to any finite number of dimensions, a rotation matrix A is an orthogonal matrix that differs from the identity matrix in at most four elements.
  • However, linear algebra includes orthogonal transformations between spaces which may be neither finite-dimensional nor of the same dimension, and these have no orthogonal matrix equivalent.
  • A similar problem, with interesting applications in shape analysis, is the orthogonal Procrustes problem, which consists of finding an orthogonal matrix which most closely maps to.
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