Lecture - Linear Algebra I MT22, VII
Flashcards
What is the Steinitz exchange lemma?
Given two sets of linearly independent vectors, it’s possible to replace the vectors of one with vectors from the other and still stay independent.
What’s the main tool in proving that two bases of a vector space must have the same amount of elements?
The Steinitz exchange lemma.
What is the dimension of any vector space $V$?
The cardinality of its basis.
What’s the dimension of $\mathbb{C}$?
It’s impossible to say without specifying the base field.
What is true about the non-zero rows of a matrix in row-echelon form?
They span a vector subspace of the original vector space.
What’s does the row space $\text{row}(A)$ of a matrix represent?
The span of the rows.
What does the column space $\text{col}(A)$ of a matrix represent?
The span of the columns.