Symmetry of Second Derivatives
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the symmetry of second derivatives (also called the equality of mixed partials) refers to the possibility of interchanging the order of taking partial derivatives of a functionof n variables. If the partial derivative with respect to xi is denoted with a subscript i, then the symmetry is the assertion that the second-order partial derivatives fij satisfy the identityso that they form an n × n symmetric matrix. This is sometimes known as Young''s theor...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the symmetry of second derivatives (also called the equality of mixed partials) refers to the possibility of interchanging the order of taking partial derivatives of a functionof n variables. If the partial derivative with respect to xi is denoted with a subscript i, then the symmetry is the assertion that the second-order partial derivatives fij satisfy the identityso that they form an n × n symmetric matrix. This is sometimes known as Young''s theorem.This matrix of second-order partial derivatives of f is called the Hessian matrix of f. The entries in it off the main diagonal are the mixed derivatives; that is, successive partial derivatives with respect to different variables.
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