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Consequence for Matrix Multiplication

• Suppose BA = I . Then BA takes the standard basis vectors to themselves.

• Let v1, v2 , and v3 be the columns of A

• is just . It also equals e1 . Same goes for e2 and e3 .

• Thus B sends the vectors v1, v2 , and v3 to the vectors e1, e2 and e3

• If BA = I , then B sends to columns of A to the three standard unit vectors.

Mathematics of Projections - 09 MAY 95

Page 33 of 44

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