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In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.The determinant of a matrix A is commonly denoted det(A), det A, or | A |.Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.
The determinant of the left hand side is the product of the determinants of the three matrices. Since the first and third matrix are triangular matrices with unit diagonal, their determinants are just 1. The determinant of the middle matrix is our desired value.
In vector calculus, the Jacobian matrix (/ dʒ ə ˈ k oʊ b i ə n /, [1] [2] [3] / dʒ ɪ-, j ɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.
Those who wish to adopt the textbooks are required to send a request to NCERT, upon which soft copies of the books are received. The material is press-ready and may be printed by paying a 5% royalty, and by acknowledging NCERT. [11] The textbooks are in color-print and are among the least expensive books in Indian book stores. [11]
Similarly, the Laplace expansion along the j th column is the equality = = +,,. (Each identity implies the other, since the determinants of a matrix and its transpose are the same.) The coefficient ( − 1 ) i + j m i , j {\displaystyle (-1)^{i+j}m_{i,j}} of b i , j {\displaystyle b_{i,j}} in the above sum is called the cofactor of b i , j ...
The most popular of which for computing functional determinants is the zeta function regularization. [1] For instance, this allows for the computation of the determinant of the Laplace and Dirac operators on a Riemannian manifold, using the Minakshisundaram–Pleijel zeta function. Otherwise, it is also possible to consider the quotient of two ...
An exemplar is a person, a place, an object, or some other entity that serves as a predominant example of a given concept (e.g. "The heroine became an exemplar in courage to the children"). It may also refer to:
The poem Sabse Khatarnak by the Hindi poet Pash was included in the NCERT textbook for 11th standard Hindi students in 2006. In 2017, the BJP government affiliated RSS tried to remove it but failed. [25] [26] The NCERT made two controversial changes to the class XII political science textbook ‘Politics in India Since Independence’ in 2017.