picos.expressions.exp_specnorm¶
Implements SpectralNorm
.
Classes
- class picos.expressions.exp_specnorm.SpectralNorm(x)[source]¶
Bases:
Expression
The spectral norm of a matrix.
This class can represent the spectral norm of a matrix-affine expression (real- or complex valued). The spectral norm is convex, so we can form expressions of the form
SpectralNorm(X) <= t
which are typically reformulated as LMIs that can be handled by SDP solvers.- Definition
If the normed expression is a matrix
, then its spectral norm is
where
denotes the largest eigenvalue of a matrix, and
denotes the adjoint matrix of
(i.e., the transposed matrix
if
is real-valued).
Special cases:
If
is scalar, then
reduces to the the absolute value (or modulus)
.
If
is scalar, then
coincides with the Euclidean norm of
.
- __init__(x)[source]¶
Construct a
SpectralNorm
.- Parameters
x (ComplexAffineExpression) – The affine expression to take the norm of.
- property x¶
Real expression whose norm equals that of the original expression.