In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A. If A is a differentiable map from the real numbers to n × n matrices,
Equivalently, if dA stands for the differential of A, the formula is
It is named after the mathematician C.G.J. Jacobi.
Read more about Jacobi's Formula: Derivation, Corollary
Famous quotes containing the words jacobi and/or formula:
“... spinsterhood [is considered to be] an abnormality of small proportions and small consequence, something like an extra finger or two on the body, presumably of temporary duration, and never of any social significance.”
—Mary Putnam Jacobi (18421906)
“I feel like a white granular mass of amorphous crystalsmy formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,with a fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor.”
—Lafcadio Hearn (18501904)