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In passive sonar, adaptive beamforming can be used to increase the array output signal-to-interference-plus-noise ratio (SINR) over delay-and-sum techniques, provided that array steering vector (ASV) and covariance matrix errors are accounted for. By exploiting ellipsoidal sets of the ASV, robust Capon beamformers (RCBs) systematically allow for ASV errors. For large aperture, many-element passive sonar arrays, the computational and sample support requirements often make element-space beamforming unfeasible and one is forced to consider reduced-dimension techniques. Here, a framework is proposed for combining reduced-dimension and RCB methods, producing rapidly converging, low complexity reduced-dimension RCBs (RDRCBs) allowing for ASV errors. The key contribution is the derivation of reduced-dimension ellipsoids, used by the RDRCBs, from typically available element-space sets and the dimension-reducing transformation(s) via propagation. The method allows for any ellipsoidal element-space ASV set and any full (column) rank dimension-reducing transformation. Here, for the application, the author considers the use of beamspace techniques within the RDRCB framework. The SINR of the RDRCBs are analysed, showing where they can outperform their element-space counter-parts. The benefits of using the RDRCBs are illustrated on experimental passive sonar data.