query: Basis and Dimension of Subspace
positive_passages.docid: 144145
positive_passages.text: Symmetric $3\times 3$ Matrices - Base matrix
negative_passages.docid: 79061
negative_passages.text: show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
negative_passages.docid: 115273
negative_passages.text: Nilpotent matrix and basis for $F^n$
negative_passages.docid: 59030
negative_passages.text: Finding the dimension of a given vector space
negative_passages.docid: 134162
negative_passages.text: What is a basis for the space of $n\times n$ Hermitian matrices?
negative_passages.docid: 138653
negative_passages.text: Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
negative_passages.docid: 4374
negative_passages.text: Geometric interpretation of a vector space and subspace?
negative_passages.docid: 158170
negative_passages.text: vector space dimension of linear varieties
negative_passages.docid: 154724
negative_passages.text: Every vector space has a basis
negative_passages.docid: 78833
negative_passages.text: Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
negative_passages.docid: 112939
negative_passages.text: Find a basis for the subspace of $\mathbb{R}^4$ spanned by the given vectors.
negative_passages.docid: 78604
negative_passages.text: How to find basis of intersection of 2 vector spaces with given basis?
negative_passages.docid: 55230
negative_passages.text: Dimension of set of commutable matrices
negative_passages.docid: 142097
negative_passages.text: Finding the dimension of the orthogonal complement
negative_passages.docid: 33188
negative_passages.text: Dimension of null space of a given problem
negative_passages.docid: 10715
negative_passages.text: Orthogonal projection and two subspaces
negative_passages.docid: 44431
negative_passages.text: The dimension of a subspace is less than dimension of the whole space.