Linear Algebra
Vectors
A vector has both magnitude and direction. Vectors are fundamental in physics and linear algebra.
Key Formulas
Dot product
Scalar product of two vectors.
Magnitude
Length of a vector.
Key Concepts
AdditionScalar multiplicationDot productCross product
Worked Examples
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Matrices
A matrix is a rectangular array of numbers used to represent linear transformations and systems.
Determinants
The determinant is a scalar value computed from a square matrix that reveals properties of the matrix.
Eigenvalues and Eigenvectors
An eigenvector of a matrix is a vector that only scales when the matrix is applied. The scaling factor is the eigenvalue.