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<html>
<head> <link rel="canonical" href="https://slepc.upv.es/documentation/current//Users/jroman/tmp/slepc-3.23.1/docs/manualpages/BV/index.html" />
  <link rel="stylesheet" href="/slepc.css" type="text/css">
  <title>Basis Vectors - BV</title>
</head>

<body class="manpageindex">
   <div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
   <div id="bugreport" align=right><a href="mailto:slepc-maint@upv.es?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: slepc-3.23.1 v3.23.1 /Users/jroman/tmp/slepc-3.23.1/docs/manualpages/BV/index.html "><small>Report Typos and Errors</small></a></div>

<h2>Basis Vectors - BV</h2>

<p>
The BV package provides the concept of a block of vectors that represent the basis of a subspace. It is a convenient way of handling a collection of vectors that often operate together, rather than working with an array of Vec.
</p>
<p>
These routines are usually not needed by application programmers.
<p>


<P>
<TABLE>
<TR><TD WIDTH=250 COLSPAN="3"><B>Beginner - Basic usage</B></TD></TR>
 <TD WIDTH=250><A HREF="./BV.html">BV</A></TD>
 <TD WIDTH=250><A HREF="./BVGetColumn.html">BVGetColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVMatMultTransposeColumn.html">BVMatMultTransposeColumn</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCopy.html">BVCopy</A></TD>
 <TD WIDTH=250><A HREF="./BVGetSizes.html">BVGetSizes</A></TD>
 <TD WIDTH=250><A HREF="./BVRestoreColumn.html">BVRestoreColumn</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCopyColumn.html">BVCopyColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVMatMult.html">BVMatMult</A></TD>
 <TD WIDTH=250><A HREF="./BVSetFromOptions.html">BVSetFromOptions</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCopyVec.html">BVCopyVec</A></TD>
 <TD WIDTH=250><A HREF="./BVMatMultColumn.html">BVMatMultColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVSetSizes.html">BVSetSizes</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCreate.html">BVCreate</A></TD>
 <TD WIDTH=250><A HREF="./BVMatMultHermitianTranspose.html">BVMatMultHermitianTranspose</A></TD>
 <TD WIDTH=250><A HREF="./BVSetSizesFromVec.html">BVSetSizesFromVec</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCreateVec.html">BVCreateVec</A></TD>
 <TD WIDTH=250><A HREF="./BVMatMultHermitianTransposeColumn.html">BVMatMultHermitianTransposeColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVType.html">BVType</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDestroy.html">BVDestroy</A></TD>
 <TD WIDTH=250><A HREF="./BVMatMultTranspose.html">BVMatMultTranspose</A></TD>
 <TD WIDTH=250><A HREF="./BVView.html">BVView</A></TD>
<TR>
<TR><TD WIDTH=250 COLSPAN="3"><B>Intermediate - Setting options for algorithms and data structures</B></TD></TR>
 <TD WIDTH=250><A HREF="./BVCreateFromMat.html">BVCreateFromMat</A></TD>
 <TD WIDTH=250><A HREF="./BVInsertVec.html">BVInsertVec</A></TD>
 <TD WIDTH=250><A HREF="./BVNormColumn.html">BVNormColumn</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCreateMat.html">BVCreateMat</A></TD>
 <TD WIDTH=250><A HREF="./BVInsertVecs.html">BVInsertVecs</A></TD>
 <TD WIDTH=250><A HREF="./BVNormalize.html">BVNormalize</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDot.html">BVDot</A></TD>
 <TD WIDTH=250><A HREF="./BVMatProject.html">BVMatProject</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthogonalize.html">BVOrthogonalize</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDotVec.html">BVDotVec</A></TD>
 <TD WIDTH=250><A HREF="./BVMult.html">BVMult</A></TD>
 <TD WIDTH=250><A HREF="./BVScale.html">BVScale</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDuplicate.html">BVDuplicate</A></TD>
 <TD WIDTH=250><A HREF="./BVMultInPlace.html">BVMultInPlace</A></TD>
 <TD WIDTH=250><A HREF="./BVScaleColumn.html">BVScaleColumn</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDuplicateResize.html">BVDuplicateResize</A></TD>
 <TD WIDTH=250><A HREF="./BVMultInPlaceHermitianTranspose.html">BVMultInPlaceHermitianTranspose</A></TD>
 <TD WIDTH=250><A HREF="./BVSetActiveColumns.html">BVSetActiveColumns</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetActiveColumns.html">BVGetActiveColumns</A></TD>
 <TD WIDTH=250><A HREF="./BVMultVec.html">BVMultVec</A></TD>
 <TD WIDTH=250><A HREF="./BVSetType.html">BVSetType</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetType.html">BVGetType</A></TD>
 <TD WIDTH=250><A HREF="./BVNorm.html">BVNorm</A></TD>
 <TD WIDTH=250><A HREF="./BVViewFromOptions.html">BVViewFromOptions</A></TD>
<TR>
<TR><TD WIDTH=250 COLSPAN="3"><B>Advanced - Setting more advanced options and customization</B></TD></TR>
 <TD WIDTH=250><A HREF="./BVAppendOptionsPrefix.html">BVAppendOptionsPrefix</A></TD>
 <TD WIDTH=250><A HREF="./BVGetSplitRows.html">BVGetSplitRows</A></TD>
 <TD WIDTH=250><A HREF="./BVRestoreArrayRead.html">BVRestoreArrayRead</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVApplyMatrix.html">BVApplyMatrix</A></TD>
 <TD WIDTH=250><A HREF="./BVGetVecType.html">BVGetVecType</A></TD>
 <TD WIDTH=250><A HREF="./BVRestoreMat.html">BVRestoreMat</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVBiorthogonalizeColumn.html">BVBiorthogonalizeColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVInsertConstraints.html">BVInsertConstraints</A></TD>
 <TD WIDTH=250><A HREF="./BVRestoreSplit.html">BVRestoreSplit</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVBiorthonormalizeColumn.html">BVBiorthonormalizeColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVMatArnoldi.html">BVMatArnoldi</A></TD>
 <TD WIDTH=250><A HREF="./BVRestoreSplitRows.html">BVRestoreSplitRows</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCreateTensor.html">BVCreateTensor</A></TD>
 <TD WIDTH=250><A HREF="./BVMatLanczos.html">BVMatLanczos</A></TD>
 <TD WIDTH=250><A HREF="./BVSetDefiniteTolerance.html">BVSetDefiniteTolerance</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDotColumn.html">BVDotColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVMatMultType.html">BVMatMultType</A></TD>
 <TD WIDTH=250><A HREF="./BVSetLeadingDimension.html">BVSetLeadingDimension</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDotColumnBegin.html">BVDotColumnBegin</A></TD>
 <TD WIDTH=250><A HREF="./BVMultColumn.html">BVMultColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVSetMatMultMethod.html">BVSetMatMultMethod</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDotColumnEnd.html">BVDotColumnEnd</A></TD>
 <TD WIDTH=250><A HREF="./BVNormColumnBegin.html">BVNormColumnBegin</A></TD>
 <TD WIDTH=250><A HREF="./BVSetMatrix.html">BVSetMatrix</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDotVecBegin.html">BVDotVecBegin</A></TD>
 <TD WIDTH=250><A HREF="./BVNormColumnEnd.html">BVNormColumnEnd</A></TD>
 <TD WIDTH=250><A HREF="./BVSetOptionsPrefix.html">BVSetOptionsPrefix</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDotVecEnd.html">BVDotVecEnd</A></TD>
 <TD WIDTH=250><A HREF="./BVNormVecBegin.html">BVNormVecBegin</A></TD>
 <TD WIDTH=250><A HREF="./BVSetOrthogonalization.html">BVSetOrthogonalization</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetArray.html">BVGetArray</A></TD>
 <TD WIDTH=250><A HREF="./BVNormVecEnd.html">BVNormVecEnd</A></TD>
 <TD WIDTH=250><A HREF="./BVSetRandom.html">BVSetRandom</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetArrayRead.html">BVGetArrayRead</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthogBlockType.html">BVOrthogBlockType</A></TD>
 <TD WIDTH=250><A HREF="./BVSetRandomColumn.html">BVSetRandomColumn</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetDefiniteTolerance.html">BVGetDefiniteTolerance</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthogRefineType.html">BVOrthogRefineType</A></TD>
 <TD WIDTH=250><A HREF="./BVSetRandomCond.html">BVSetRandomCond</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetLeadingDimension.html">BVGetLeadingDimension</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthogType.html">BVOrthogType</A></TD>
 <TD WIDTH=250><A HREF="./BVSetRandomContext.html">BVSetRandomContext</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetMat.html">BVGetMat</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthogonalizeColumn.html">BVOrthogonalizeColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVSetRandomNormal.html">BVSetRandomNormal</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetMatMultMethod.html">BVGetMatMultMethod</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthogonalizeSomeColumn.html">BVOrthogonalizeSomeColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVSetRandomSign.html">BVSetRandomSign</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetMatrix.html">BVGetMatrix</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthogonalizeVec.html">BVOrthogonalizeVec</A></TD>
 <TD WIDTH=250><A HREF="./BVSetVecType.html">BVSetVecType</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetNumConstraints.html">BVGetNumConstraints</A></TD>
 <TD WIDTH=250><A HREF="./BVOrthonormalizeColumn.html">BVOrthonormalizeColumn</A></TD>
 <TD WIDTH=250><A HREF="./BVTensorBuildFirstColumn.html">BVTensorBuildFirstColumn</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetOptionsPrefix.html">BVGetOptionsPrefix</A></TD>
 <TD WIDTH=250><A HREF="./BVRegister.html">BVRegister</A></TD>
 <TD WIDTH=250><A HREF="./BVTensorCompress.html">BVTensorCompress</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetOrthogonalization.html">BVGetOrthogonalization</A></TD>
 <TD WIDTH=250><A HREF="./BVRegisterAll.html">BVRegisterAll</A></TD>
 <TD WIDTH=250><A HREF="./BVTensorGetDegree.html">BVTensorGetDegree</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetRandomContext.html">BVGetRandomContext</A></TD>
 <TD WIDTH=250><A HREF="./BVResize.html">BVResize</A></TD>
 <TD WIDTH=250><A HREF="./BVTensorGetFactors.html">BVTensorGetFactors</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetSplit.html">BVGetSplit</A></TD>
 <TD WIDTH=250><A HREF="./BVRestoreArray.html">BVRestoreArray</A></TD>
 <TD WIDTH=250><A HREF="./BVTensorRestoreFactors.html">BVTensorRestoreFactors</A></TD>
<TR>
<TR><TD WIDTH=250 COLSPAN="3"><B>Developer - Interfaces intended primarily for library developers, not for typical applications programmers</B></TD></TR>
 <TD WIDTH=250><A HREF="./BVApplyMatrixBV.html">BVApplyMatrixBV</A></TD>
 <TD WIDTH=250><A HREF="./BVGetCachedBV.html">BVGetCachedBV</A></TD>
 <TD WIDTH=250><A HREF="./BVScatter.html">BVScatter</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCISSResizeBases.html">BVCISSResizeBases</A></TD>
 <TD WIDTH=250><A HREF="./BVGetSignature.html">BVGetSignature</A></TD>
 <TD WIDTH=250><A HREF="./BVSetBufferVec.html">BVSetBufferVec</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVCreateVecEmpty.html">BVCreateVecEmpty</A></TD>
 <TD WIDTH=250><A HREF="./BVInitializePackage.html">BVInitializePackage</A></TD>
 <TD WIDTH=250><A HREF="./BVSetNumConstraints.html">BVSetNumConstraints</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVDotQuadrature.html">BVDotQuadrature</A></TD>
 <TD WIDTH=250><A HREF="./BVNormVec.html">BVNormVec</A></TD>
 <TD WIDTH=250><A HREF="./BVSetSignature.html">BVSetSignature</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVFinalizePackage.html">BVFinalizePackage</A></TD>
 <TD WIDTH=250><A HREF="./BVSVDAndRank.html">BVSVDAndRank</A></TD>
 <TD WIDTH=250><A HREF="./BVSumQuadrature.html">BVSumQuadrature</A></TD>
<TR>
 <TD WIDTH=250><A HREF="./BVGetBufferVec.html">BVGetBufferVec</A></TD>
 <TD WIDTH=250><A HREF="./BVSVDMethod.html">BVSVDMethod</A></TD>
 <TD WIDTH=250><A HREF="./BVTraceQuadrature.html">BVTraceQuadrature</A></TD>
<TR>
<TR><TD WIDTH=250 COLSPAN="3"><B>No deprecated routines</B></TD></TR>
</TABLE>
<BR><A HREF="../../../docs/manual.html">Table of Contents</A>