4.3 COORDINATES IN A LINEAR SPACE By introducing
... The B coordinate transformation T (f ) = [f ]B from V to Rn is an isomorphism (i.e., an invertible linear transformation). Thus, V is isomorphic to Rn; the linear spaces V and Rn have the same structure. Example. Choose a basis of P2 and thus transform P2 into Rn, for an appropriate n. Example. Let ...
... The B coordinate transformation T (f ) = [f ]B from V to Rn is an isomorphism (i.e., an invertible linear transformation). Thus, V is isomorphic to Rn; the linear spaces V and Rn have the same structure. Example. Choose a basis of P2 and thus transform P2 into Rn, for an appropriate n. Example. Let ...
Chapter 3
... More about matrix multiplication: 1) The product is associative: A(BC)=(AB)C 2) The product is distributive: A(B+C)=AB+AC 3) In general the product is not commutative: ABBA. [A,B]=AB−BA is called the commutator. Unit matrix: ...
... More about matrix multiplication: 1) The product is associative: A(BC)=(AB)C 2) The product is distributive: A(B+C)=AB+AC 3) In general the product is not commutative: ABBA. [A,B]=AB−BA is called the commutator. Unit matrix: ...
