Linear Algebra Flashcards
What is the matrix representation of the Hadamard rotation?
What is the “complete eigenvector decomposition” of a (normal) matrix.
The matrix is diagonalised: written as a sum of its eigenvectors.
Prove the following triangle inequality.
Take the square root of this argument.
What is the parallelogram identity?
What is the polarisation identity?
How do you prove the Cauchy-Schwartz Inequality?
What are the three Pauli matrices?
How do you extract matrix elements from an operator?
How do you express a basis vector as a sum of another set of basis vectors?
How does an operator change under a transformation of basis?
What are the dimensionality of Hilbert spaces under tensor-sums and tensor-products.
How are state vectors in a tensor product represented as a sum over eigenstates?
How do inner products work with tensor-sums and tensor-products?
How do we define a tensor power?
How would you apply a Hadamard rotation to this vector?
How do you apply a Hadamard roation to a general vector?
What are the matrix representations of tensor sums & products?
What are the eigenvalues & eigenvectors of tensor sums and tensor products?
What is the Cauchy-Schwarz inequality?
