An audio signal downmixing apparatus for processing an input audio signal comprising a plurality of input channels into an output audio signal comprising a plurality of primary output channels and at least one auxiliary output channel using a downmix matrix, wherein the downmix matrix comprises a primary downmix matrix (D U) for providing the plurality of primary output channels and an auxiliary downmix matrix (D W) for providing the at least one auxiliary output channel, the audio signal downmixing apparatus comprising: an auxiliary downmix matrix determiner configured to determine the auxiliary downmix matrix (D W) by: computing a plurality of eigenvectors of a covariance matrix defined by the plurality of input channels of the input audio signal; determining for at least one eigenvector of the plurality of eigenvectors of the covariance matrix a subspace angle between the at least one eigenvector and a vector defined by a column of the primary downmix matrix (D U); selecting at least one eigenvector from the plurality of eigenvectors based on the subspace angle and a preset threshold angle θ MIN; and defining at least one column of the auxiliary downmix matrix (D W) by the at least one selected eigenvector; and a processor configured to process the input audio signal into the output audio signal using the downmix matrix; wherein the auxiliary downmix matrix determiner is configured to determine the subspace angle by determining the smallest angle of a plurality of angles between each eigenvector of the plurality of eigenvectors of the covariance matrix and the plurality of vectors defined by the columns of the primary downmix matrix (D U); wherein the auxiliary downmix matrix determiner is configured to select at least one eigenvector from the plurality of eigenvectors based on the subspace angle and the preset threshold angle θ MIN by selecting at least one eigenvector, for which the subspace angle is bigger than the preset threshold angle θ MIN. an auxiliary downmix matrix determiner configured to determine the auxiliary downmix matrix (D W) by: computing a plurality of eigenvectors of a covariance matrix defined by the plurality of input channels of the input audio signal; determining for at least one eigenvector of the plurality of eigenvectors of the covariance matrix a subspace angle between the at least one eigenvector and a vector defined by a column of the primary downmix matrix (D U); selecting at least one eigenvector from the plurality of eigenvectors based on the subspace angle and a preset threshold angle θ MIN; and defining at least one column of the auxiliary downmix matrix (D W) by the at least one selected eigenvector; and computing a plurality of eigenvectors of a covariance matrix defined by the plurality of input channels of the input audio signal; determining for at least one eigenvector of the plurality of eigenvectors of the covariance matrix a subspace angle between the at least one eigenvector and a vector defined by a column of the primary downmix matrix (D U); selecting at least one eigenvector from the plurality of eigenvectors based on the subspace angle and a preset threshold angle θ MIN; and defining at least one column of the auxiliary downmix matrix (D W) by the at least one selected eigenvector; and a processor configured to process the input audio signal into the output audio signal using the downmix matrix; wherein the auxiliary downmix matrix determiner is configured to determine the subspace angle by determining the smallest angle of a plurality of angles between each eigenvector of the plurality of eigenvectors of the covariance matrix and the plurality of vectors defined by the columns of the primary downmix matrix (D U); wherein the auxiliary downmix matrix determiner is configured to select at least one eigenvector from the plurality of eigenvectors based on the subspace angle and the preset threshold angle θ MIN by selecting at least one eigenvector, for which the subspace angle is bigger than the preset threshold angle θ MIN.