all fit into the same story. More generally, whenever some functor "forgets" some data or structure and has a left adjoint, that left adjoint will have a "free" flavor to it. What about the counit? So far the discussion has been about the unit of an adjunction. I'll say a few ...
transpose(mat<T,M,N> a) -> mat<T,N,M> is the transpose of matrix a adjugate(mat<T,N,N> a) -> mat<T,N,N> is the adjugate or classical adjoint of matrix a (the transpose of its cofactor matrix, or the numerator in the expression of its inverse) comatrix(mat<T,N,N> a)...
The rest of the work has already been done by the library with operator overloading.Here is an example program that differentiates a complicated function:#include <fastad> #include <iostream> int main() { using namespace ad; ForwardVar<double> w1(0.), w2(1.); w1.set_adjoint(1.); ...
The matrices[10−3|80215|−9015|−2]and[10−3|8005|−5015|−2]row equivalent. What is the row operation that transforms the first matrix to the second? Row Operations: Row operations on augmented matrices include multiplying a row by a constant, ...
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A=⎡⎢⎣a101bd1bc⎤⎥⎦then find the value of |A| View Solution If A=[2 5 7 90 1 9 70 0 -1 80 0 0 1]then the value of|adj(adjA)|is View Solution IfAis a square matrix of order 3 such that|A|=5, write the value of|adjA|. ...
u.transpose : 2x2-matrix: ⎛1.0 3.0 ⎞ ⎝2.0i 1.0 + 4.0i⎠ u.adjoint : 2x2-matrix: ⎛1.0 3.0 ⎞ ⎝-2.0i 1.0 - 4.0i⎠ The adjoint has the advantage over the transpose that many properties involving the adjoint generalize naturally from real matrices to complex matrices. ...
transpose(mat<T,M,N> a) -> mat<T,N,M> is the transpose of matrix a adjugate(mat<T,N,N> a) -> mat<T,N,N> is the adjugate or classical adjoint of matrix a (the transpose of its cofactor matrix, or the numerator in the expression of its inverse) comatrix(mat<T,N,N> a)...
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The rest of the work has already been done by the library with operator overloading.Here is an example program that differentiates a complicated function:#include <fastad> #include <iostream> int main() { using namespace ad; ForwardVar<double> w1(0.), w2(1.); w1.set_adjoint(1.); ...