## Dual Vector Space

##### November 12, 2020

The space of all linear functionals \(f:V\rightarrow \mathbb{R}\), noted as \(V^{*}\) The dual space has the same …

The space of all linear functionals \(f:V\rightarrow \mathbb{R}\), noted as \(V^{*}\) The dual space has the same …

The bubble, created by the Sun’s plasma (see Solar Wind), which encompasses the Sun itself. Outside of this …

TODO

As a linear representation # A tensor can be represented as a vector of x-number of dimensions. Basically, a … ...

\begin{equation} \delta_{ij}= \begin{cases} 0 & \text{if i \(\neq\) j}\\\ 1 & \text{if i \(=\) j} \end{cases} …

a basis for an n-dimensional vector space \(V\) is any ordered set of linearly independent vectors \((\mathbf{e}_{1}, …

An orthonormal basis is a basis where all the vectors are one unit long and all perpendicular to each other (e.g. the …

Consider two bases \((\mathbf{e}_{1},\mathbf{e}_{2})\) and \((\mathbf{\tilde{e}}_{1},\mathbf{\tilde{e}}_{2})\), where we … ...

\begin{equation} \mathbf{I}(\mathbf{X})=\mathbf{X} \end{equation} Where any \(nxn\) matrix is established via the …

A matrix, which when multiplied by another matrix, results in the identity matrix. \begin{equation} …