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The determinant via

The determinant via permutations

The determinant as

The determinant as a product of eigenvalues

The trace is

The trace is basis-invariant

The trace and

The trace and the eigenvalues

Properties of the

Properties of the Riesz element

An abstract explicit

An abstract explicit isomorphism between vector spaces

Stating and applying

Stating and applying the complex spectral theorem

A normal operator

A normal operator that is not self-adjoint

A property of

A property of the image of a self-adjoint operator

Determining self-adjointness from

Determining self-adjointness from the matrix

The adjoint of

The adjoint of a composition

Finding the image

Finding the image of the adjoint map

Invertible diagonal matrix

Invertible diagonal matrix with indistinct diagonal entries

Finding the matrix

Finding the matrix of the operator given an eigenvalue

Explicitly finding the

Explicitly finding the orthogonal complement

Orthogonal complements reverse

Orthogonal complements reverse subset containment

Proof of the

Proof of the Existence of Riesz elements

Applying the (modified)

Applying the (modified) Gram–Schmidt method

Upper-triangular with respect

Upper-triangular with respect to an orthonormal basis

Finding eigenvalues and

Finding eigenvalues and eigenvectors at the same time

Pulling a scalar

Pulling a scalar out of a norm

Orthogonality of the

Orthogonality of the orthogonal decomposition

Verifying the inner-product

Verifying the inner-product axioms

The transpose is

The transpose is a linear isomorphism