Wilkinson Microwave Anisotropy Probe

Product Name
Inverse Covariance Matrices
Coord. System
Projection Type
HEALPix, nested, Res 4/NSide=16


The inverse covariance (N-1) matrices supplied with the higher resolution maps do not fullly characterize the pixel-to-pixel noise in the res 4 maps. Therefore a more accurate and much larger inverse covariance matrix is supplied for each map as a separate product. These are supplied in one of two forms:

  • A 6144x6144 matrix containing four 3072x3072 blocks representing Q-U covariance with the form:

    Most of the matrices supplied have this form.
  • A 12288x12288 matrix containing sixteen 3072x3072 blocks representing I-Q-U-S covariance with the form:

    These matrices are supplied for the single year IQUS maps per differencing assembly.

All the inverse covariance matrices have had σ02 divided out of them. These factors may be found in skymap_info.cfm.

The elements corresponding to the Galatic plane pixels as defined by the processing mask were set to zero. Therefore, the matrices as supplied are singular. To make them non-singular, the row and the column corresponding to each zero element of the diagonal need to be deleted.

The matrices include a contribution due to uncertainty in the loss imbalance coefficients in each differencing assembly (Jarosik et al. 2010). In previous releases, this uncertainty was fully marginalized--equivalent to assuming no information about these coefficients. In the latest release of the matrices for raw Stokes Q and U maps (those without foreground cleaning), a true 1-σ uncertainty was incorporated into this term.

Additional Information

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