Please enable JavaScript.
Coggle requires JavaScript to display documents.
linear algebra - Coggle Diagram
linear algebra
vector
definition
2d, has lengh and direction
-
in math, the generalizatio of physical and cs views
note: in linear algebra, vector only starts from [0, 0]
-
-
-
-
linear combination, span and basis vector
basis vector
\(\hat{i} , \hat{j}\): unit vector in x and y direction, length = 2
linear combination: \( a\mathbf{v}+b\mathbf{w}, a\,and\,b \in \mathbb{R} \)
span: the span of \( \hat{v}\,and\,\hat{j} \) is the set of all their linear combinations
\( \hat{v} \, and \, \hat{w} \neq 0\), and they are linear independent, span is the plane
one of \( \hat{v}, \hat{w} = 0\), or they are linear dependent, the span is the line
\( \hat{v} \, and \, \hat{w} = 0\), the span is the origin
technical definition of basis: the basis of a vector space is a set of linear independent vector that can sspan the full space
-