Let L be a linear operator on a vector space V . Let A be the matrix representing L with respect to an ordered basis { v 1 , ... , v n } of V [i.e., L ( v j ) = ∑ i = 1 n a i j v i , j = 1 , ... , n ]. Show that A m is the matrix representing L m with respect to { v 1 , ... , v n } .
Let L be a linear operator on a vector space V . Let A be the matrix representing L with respect to an ordered basis { v 1 , ... , v n } of V [i.e., L ( v j ) = ∑ i = 1 n a i j v i , j = 1 , ... , n ]. Show that A m is the matrix representing L m with respect to { v 1 , ... , v n } .
Solution Summary: The author explains that matrix A represents linear operator L on a vector space V for every min N.
Let L be a linear operator on a vector space V. Let A be the matrix representing L with respect to an ordered basis
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of V [i.e.,
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Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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