Inverse of upper triangular matrices
Inverse of an invertible upper triangular matrix of order 3
There is a nice trick for calculating the inverse of any invertible upper triangular matrix, one which avoids the computation of complicated determinants.
There is a nice trick for calculating the inverse of any invertible upper triangular matrix, one which avoids the computation of complicated determinants.
Direct sum isomorphic to sum
Direct sum isomorphic to sum?
The direct sum of two subspaces of $E$ is an abstract vector space that has a canonical map to $E$, but that map can fail to be injective, and it will precisely when the two subspaces have non-zero intersection. So your mistake is in assuming that the direct sum is a subspace of $E$.
The direct sum of two subspaces of $E$ is an abstract vector space that has a canonical map to $E$, but that map can fail to be injective, and it will precisely when the two subspaces have non-zero intersection. So your mistake is in assuming that the direct sum is a subspace of $E$.
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