Master Linear Algebra Essentials with 120 free flashcards. Study using spaced repetition and focus mode for effective learning in General.
A single real (or complex) number, as opposed to a vector or matrix.
An ordered list of scalars; geometrically, a directed magnitude in space.
A rectangular array of numbers arranged in rows and columns.
A multi-dimensional array that generalizes scalars (0-D), vectors (1-D), and matrices (2-D) to higher orders.
The number of vectors in any basis of the space, written dim(V).
A sum of scalar multiples of the vectors: c₁v₁ + c₂v₂ + ... + cₙvₙ.
A set of vectors is linearly independent if no vector in the set can be written as a linear combination of the others; equivalently, c₁v₁+...+cₙvₙ=0 implies all cᵢ=0.
A set of vectors is linearly dependent if there exist scalars, not all zero, such that their linear combination equals the zero vector.
A linearly independent set of vectors that spans the entire space.
The set of all linear combinations of those vectors; it is itself a vector subspace.
A non-empty subset closed under vector addition and scalar multiplication, containing the zero vector.
The span of its columns, i.e. {Ax : x ∈ ℝⁿ}; a subspace of ℝᵐ.
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