Thread: Vector algebra
A few topics about multidimensional vectors and matrices
- Vectors and their products
- An introduction to vectors
- Vectors in two- and three-dimensional Cartesian coordinates
- Vectors in arbitrary dimensions
- Examples of n-dimensional vectors
- The dot product
- The formula for the dot product in terms of vector components
- Dot product examples
- The cross product
- The formula for the cross product
- Cross product examples
- The scalar triple product
- Scalar triple product example
- Matrices
- Introduction to matrices
- Multiplying matrices and vectors
- Matrix and vector multiplication examples
- The transpose of a matrix
- Dot product in matrix notation
- Linear transformations
- Matrices and linear transformations
- Matrices and determinants for multivariable calculus
- The relationship between determinants and area or volume
- Determinants and linear transformations
- Geometric properties of the determinant
- How linear transformations map parallelograms and parallelepipeds
- Lines and planes
- Visualizing functions in higher dimensions
- Coordinate systems
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