Explanations
Browse explanation pages that build intuition clearly and then connect the idea to notation, graphs, calculators, and formal reasoning.
Showing 5 explanations in Linear Algebra.
What eigenvectors and eigenvalues mean geometrically
An eigenvector is a direction that survives a linear transformation without rotating away from its own line. The eigenvalue tells you the scale and possible sign flip along that direction.
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What linear independence means geometrically
Linear independence is the condition that nothing in the list is wasted. Geometrically, each new vector must add a new direction instead of repeating one you already had.
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What a basis does in linear algebra
A basis is what turns a vector space into something you can navigate. It reaches every vector, and it does so without redundancy, so coordinates become possible.
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How a linear transformation changes the plane
A linear transformation of the plane is completely determined by where it sends the two standard basis vectors. From there, every grid point follows by the same linear combination.
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What a determinant measures geometrically
The determinant of a 2 by 2 matrix is the signed area scale factor of the transformation. It tells whether the unit square stretches, flips, or collapses.
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