Linear-1 8

Dimension theorem theorem


Uniqueness of linear combination lemma


Matrix spaces definition

Example


Matrix multiplication narrows its spaces lemma


Column space and equations system lemma


Column space and row space dimensions lemma


Matrix rank definition


Matrix multiplication reduces rank lemma


Invertible matrix multiplication does not reduce rank lemma


Row-equality is equivalent to rank equality lemma


Invertible matrix is full-ranked lemma


Dimension theorem for matrices lemma