- then a
basis of V
called an
eigenbasis can be
formed from
linearly independent eigenvectors of T. When T
admits an
eigenbasis, T is diagonalizable. If λ...
-
language of operators, an
integral transform—which
changes the
basis to an
eigenbasis of eigenfunctions:
which makes the
equation separable. An
important example...
- In
linear algebra,
linear transformations can be
represented by matrices. If T {\displaystyle T} is a
linear transformation mapping R n {\displaystyle...
- A, one must
first find its eigenvalues, and then find an
orthonormal eigenbasis.
Calculation reveals that the
eigenvalues of A are λ 1 = 1 , λ 2 = 9 {\displaystyle...
- {B}}} , so the
representation of B ^ {\displaystyle {\hat {B}}} in the
eigenbasis of A ^ {\displaystyle {\hat {A}}} is not a
diagonal but a
block diagonal...
- the
eigendecomposition of a
square normal matrix with an
orthonormal eigenbasis to any m × n {\displaystyle m\times n} matrix. It is
related to the...
-
measurement in the { | 0 ⟩ , | 1 ⟩ } {\displaystyle \{|0\rangle ,|1\rangle \}}
eigenbasis of A,
there are two
possible outcomes,
occurring with
equal probability:...
-
eigenbasis for the spin in the Z-direction,
whereas the
Hadamard basis { | + ⟩ , | − ⟩ } {\displaystyle \{|+\rangle ,|-\rangle \}} is the
eigenbasis for...
-
functional data.
Using this method, a
random function is
represented in the
eigenbasis,
which is an
orthonormal basis of the
Hilbert space L2 that
consists of...
- theorem, real
symmetric matrices and
complex Hermitian matrices have an
eigenbasis; that is,
every vector is
expressible as a
linear combination of eigenvectors...
