Скачать или смотреть Determinants -1 |Sitaram kaswa|Agriculture Maths|ICAR|BHU|Dairy Tech.|Food tech.|JEE| IIT|12th|11th

Determinants -1 |Sitaram kaswa|Agriculture Maths|ICAR|BHU|Dairy Tech.|Food tech.|JEE| IIT|12th Maths|11th Maths| सारणिक


In linear algebra, the determinant is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix. The determinant of a matrix A is denoted det(A), det A, or |A|. Geometrically, it can be viewed as the volume scaling factor of the linear transformation described by the matrix. This is also the signed volume of the n-dimensional parallelepiped spanned by the column or row vectors of the matrix. The determinant is positive or negative according to whether the linear transformation preserves or reverses the orientation of a real vector space.

In the case of a 2 × 2 matrix the determinant may be defined as

Similarly, for a 3 × 3 matrix A, its determinant is



Each determinant of a 2 × 2 matrix in this equation is called a minor of the matrix A. This procedure can be extended to give a recursive definition fhroughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and the determinant can be used to solve those equations, although other methods of solution are much more computationally efficient. In linear algebra, a matrix (with entries in a field) is singular (not invertible) if and only if its determinant is zero. This leads to the use of determinants in defining the characteristic polynomial of a matrix, whose roots are the eigenvalues. In analytic geometry, determinants express the signed n-dimensional volumes of n-dimensional parallelepipeds. This leads to the use of determinants in calculus, the Jacobian determinant in the change of variables rule for integrals of functions of several variables. Determinants appear frequently in algebraic identities such as the Vandermonde identity.

Determinants possess many algebraic properties. One of them is multiplicativity, namely that the determinant of a product of matrices is equal to the product of determinants. Special types of matrices have special determinants; for example, the determinant of an orthogonal matrix is always plus or minus one, and the determinant of a complex Hermitian matrix is always real.

#Determinants
#SitaramKasw
#AgricultureMaths
#ICAR
#BHU
#DairyTech.
#FoodTech.
#JEE
#IIT
#12thMaths
#11thMaths
#सारणिक