Here B , V and U are matrices: Do relation B ( V + U ) B &

Tristian Velazquez

Tristian Velazquez

Answered question

2022-06-10

Here B, V and U are matrices:
Do relation B ( V + U ) B 1 = B V B 1 + B U B 1 hold true?

Answer & Explanation

Jaylee Dodson

Jaylee Dodson

Beginner2022-06-11Added 22 answers

Step by step, and naming the properties:
B ( U + V ) B 1 = B [ ( U + V ) B 1 ] ] associative = B [ U B 1 + V B 1 ] right distributive = B V B 1 + B U B 1 left distributive In conjunction with the fact (which you can easily prove) that B ( λ A ) B 1 = λ B A B 1 , this indeed makes the map γ B ( A ) = B A B 1 a linear transformation over GL n ( R ) (invertible n × n matrices with coeff. in R . In fact it preserves products too! This action is called conjugation by the matrix B.

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