If You Can, You Can Basis
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This article deals mainly with finite-dimensional vector spaces. check my site A be the matrix of the
a
i
,
j
{\displaystyle a_{i,j}}
, and
The formula can be proven by considering the decomposition of the vector x on the two bases: one has
The change-of-basis formula results then from the uniqueness of the decomposition of a vector over a basis, here
B
old
{\displaystyle B_{\text{old}}}
find more that is
If one replaces the field occurring in the definition of a vector space by a ring, one gets the definition of a module.
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