# Category:Linear Transformations on Hilbert Spaces

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This page contains results about linear transformations on Hilbert spaces.

Definitions specific to this category can be found in Definitions/Linear Transformations on Hilbert Spaces.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

### A

### E

### P

### R

## Pages in category "Linear Transformations on Hilbert Spaces"

The following 67 pages are in this category, out of 67 total.

### B

### C

- Characterization of Finite Rank Operators
- Characterization of Invariant Subspaces
- Characterization of Normal Operators
- Characterization of Projections
- Characterization of Reducing Subspaces
- Characterization of Unitary Operators
- Classification of Bounded Sesquilinear Forms
- Closure of Range of Compact Linear Transformation is Separable
- Compact Hermitian Operator has Countable Point Spectrum
- Compact Idempotent is of Finite Rank
- Compact Linear Transformation is Bounded
- Compact Linear Transformations Composed with Bounded Linear Operator
- Compact Operator on Hilbert Space Direct Sum
- Complementary Idempotent is Idempotent
- Complementary Projection is Projection
- Condition for Nonzero Eigenvalue of Compact Operator
- Condition for Nonzero Eigenvalue of Compact Operator/Corollary
- Continuity of Linear Functionals
- Continuity of Linear Transformations

### D

### E

- Eigenspace for Normal Operator is Reducing Subspace
- Eigenvalues of Hermitian Operator are Real
- Eigenvalues of Hermitian Operator have Orthogonal Eigenspaces
- Eigenvalues of Normal Operator have Orthogonal Eigenspaces
- Equivalence of Definitions of Norm of Linear Functional
- Equivalence of Definitions of Norm of Linear Functional/Corollary
- Equivalence of Definitions of Norm of Linear Transformation

### F

### K

- Kernel of Linear Transformation is Orthocomplement of Image of Adjoint
- Kernel of Linear Transformation is Orthocomplement of Image of Adjoint/Corollary
- Kernel of Normal Operator is Kernel of Adjoint
- Kernel of Normal Operator is Orthocomplement of Image
- Kernel of Orthogonal Projection on Closed Linear Subspace of Hilbert Space

### L

### N

### O

- Operator Commuting with Diagonalizable Operator
- Operator Diagonalizable iff Basis of Eigenvectors
- Operator Zero iff Inner Product Zero
- Orthogonal Projection on Closed Linear Subspace of Hilbert Space is Bounded
- Orthogonal Projection on Closed Linear Subspace of Hilbert Space is Linear Transformation
- Orthogonal Projection on Closed Linear Subspace of Hilbert Space is Projection
- Orthogonal Projection onto Closed Linear Span

### R

### S

- Space of Bounded Linear Transformations is Banach Space
- Space of Compact Linear Transformations is Banach Space
- Spectral Theorem for Compact Hermitian Operators
- Sum of Bounded Linear Transformations is Bounded Linear Transformation
- Sum of Projections
- Sum of Projections/Binary Case
- Sum of Projections/General Case
- Surjection that Preserves Inner Product is Linear