Question

This is a TRUE-FALSE Question with justification. If Q is an orthogonal n×n matrix, then Row(Q)...

This is a TRUE-FALSE Question with justification.

  1. If Q is an orthogonal n×n matrix, then Row(Q) = Col(Q).

The Answer to this is TRUE. I want to know a solid reasoning/explanation for it.

In one of the answers, it says that " Since Q is orthogonal, QTQ = I, so Q is invertible, hence Row(Q) = Col(Q) = Rn. But my question is: Why is it that for an invertible matrix, Row(Q) = Col (Q) ?

Any other explanation that is understandable will also help.

Thanks.

Math   Advanced-Math   
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Answer #1

It is to be noted that any space generated by n independent vectors of Rn is Rn​​​​​​. As space is a subspace of Rn (as the vectors are independent) and having dimension n.

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