Differential-Geometry

## Linear Algebra

Bases Bases Transformation Coordinate Transformation Covectors Dual Space Identity Matrix Invertible Matrix Invertible Matrix Orthonormal Basis Tensor Product Tensors Vector Space Axioms (Vector Space)

## Tensors

As a linear representation # A tensor can be represented as a vector of x-number of dimensions. Basically, a generalization on top of scalars, vectors, and matrices. The specific “flavor” of the tensor (i.e. is it a scalar, vector, or matrix) is clarified by referring to the tensor’s “rank”. For instance; a rank 0 tensor is a scalr, rank 1 tensor is a one-dimensional vector, a rank 2 tensor is a two-dimensional vector ($$2x2$$ matrix), etc. ...