triangular matrixの例文

• A orthogonal or unitary matrix, and a triangular matrix.
• A triangular matrix is one that is either lower triangular or upper triangular.
• The determinant of a triangular matrix equals the product of the diagonal entries.
• The product of a Hessenberg matrix with a triangular matrix is again Hessenberg.
• Let be a normal upper triangular matrix.
• Hence, the lower triangular matrix " L " we are looking for is calculated as
• Then by Schur decomposition it is unitary similar to an upper-triangular matrix, say,.
• It results in a " unit lower triangular " matrix and an upper triangular matrix.
• The eigenvalues of a triangular matrix are listed on the diagonal, and the eigenvalue problem is solved.
• Then " S " is an upper-triangular matrix with all diagonal entries being positive.
• But then must be diagonal, for, as noted above, a normal upper-triangular matrix is diagonal.
• For example, a real triangular matrix has its eigenvalues along its diagonal, but in general is not symmetric.
• The factorization is stored as a lower triangular matrix, with the elements in the upper triangle set to zero.
• The application of the Gram Schmidt process to the column vectors of a full column orthogonal and a triangular matrix ).
• The Crout algorithm is slightly different and constructs a lower triangular matrix and a " unit upper triangular " matrix.
• The determinant of the ( upper ) triangular matrix " D " is the product of its entries on the main diagonal :.
• Using these operations, a matrix can always be transformed into an upper triangular matrix, and in fact one that is in row echelon form.
• The LU decomposition factorizes a matrix into a lower triangular matrix " L " and an upper triangular matrix " U ".
• The LU decomposition factorizes a matrix into a lower triangular matrix " L " and an upper triangular matrix " U ".
• We transform the matrix " A " into an upper triangular matrix " U " by eliminating the entries below the main diagonal.