Orthogonal and symmetric maps: Orthogonal maps
Orthogonal maps and orthogonal bases
Let #V# be an inner product space of finite dimension and let #L:V\to V# be a linear map. What is the smallest #k# for which the following statement is true?
"The map #L# is orthogonal if and only if, for every orthonormal system #\basis{\vec{a}_1,\ldots,\vec{a}_n}# in #V# of size #n\leq k#, the system #L(\vec{a}_1),\ldots,L(\vec{a}_n)# is orthonormal."
#k=# |
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