Dashboard
Featured nodes
Roots
Public root
Templates
Test template
iCorps template
Guanyu's Latex template
Ivar's latex template
Family Tree template
Latex template
Router template
Trees
Public trees
Orphans
Browse orphan nodes
Related nodes
Parents
1
Linear (in)dependence
Siblings
17
Sort by title
Sort by date
Definition of linear dependence relation on a set of vectors
Definition of trivial linear dependence relation on a set of vectors
Determine if a particular set of vectors in R^3 in linearly independent
Definition of linearly independent set of vectors: if a linear combination is 0
Theorem: a set of vectors is linearly dependent if and only if one of the vectors can be written as a linear combination of the other vectors
Definition of linearly dependent set of vectors: one of the vectors can be written as a linear combination of the other vectors
Theorem: a set of vectors is linearly independent if and only if whenever a linear combination is 0
A set of vectors is linearly independent if and only if the homogeneous linear system corresponding to the matrix of column vectors has only the trivial solution.
A set of vectors is linearly independent if and only if the matrix of column vectors in reduced row-echelon form has every column as a pivot column.
If a set of vectors contains the 0 vector
A set of two vectors is linearly dependent if and only if neither is a scalar multiple of the other.
If a set of vectors in R^n (or C^n) contains more than n elements
A subset of a linearly independent set is linearly independent.
A set is linearly independent if and only if the set of coordinate vectors with respect to any basis is linearly independent.
Removing a linearly dependent vector from a set does not change the span of the set.
Adjoining an element not in the span of a linearly independent set gives another linearly independent set.
Any linearly independent set can be expanded to a basis for the (sub)space
Knowen
β
Help
Welcome to Knowen!
Edit test node (no login required)
Create new test node (no login required)
Not logged in
Sign in
Sign up
Go to node
3
Privacy
Edit node
Definition of trivial linear dependence relation on a set of vectors
Created over 8 years ago
A
−
A
+
Put content here.
Parents
Linear (in)dependence