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in particular, the vectors are linearly independent if and only if the gram determinant is nonzero (if and only if the gram matrix is nonsingular).
en particular, los vectores son linealmente independientes si y sólo si el determinante de gram no es nulo (es decir, si la matriz de gram es invertible).
in the case of a function of a single variable, the hessian is simply the second derivative, viewed as a 1×1-matrix, which is nonsingular if and only if it is not zero.
en el caso de una función real de una variable real, el hessiano es simplemente la segunda derivada, y la no singularidad es equivalente a ser diferente de cero.
"y" is nonsingular at "p" if "y" satisfies a jacobian condition: if "m" = (∂"fi"/∂"xj") is the matrix of partial derivatives of the defining equations of the variety, then the rank of the matrix found by evaluating "m" at "p" is "n" − dim "y".
"y" is nonsingular at "p" if "y" satisfies a jacobian condition: if "m" = (∂"fi"/∂"xj") is the matrix of partial derivatives of the defining equations of the variety, then the rank of the matrix found by evaluating "m" at "p" is "n" − dim "y".