• SJSU Singular Matrix Database

    These matrices are from the University of Florida Sparse Matrix Collection. The matrices all have a structural rank that is less than min(m,n) where the matrix is m by n. Since the numerical rank is always less than or equal to the structural rank, these matrices are numerically singular by our definition. However, due to computational limitations, we have not yet successfully calculated a numerical rank or have not accurately calculated a partial singular value spectrum for these matrices.

    The statistics in the table below, the matrix id's (UFid) and the download links are from the University of Florida Sparse Matrix Collection. The matrices in the table are ordered by increasing values of max(m,n).

    singular
    value
    spectrum
    thumbnail
    Group /
    Name
    UFid down-
    load
    # rows # cols struct.
    rank
    num.
    rank
    dim
    null
    space
    num.
    rank /
    min(m,n)
    condest gap nnz /
    (m*n)
    type
    ? Pajek/
    FA
    1472 MAT,
    MM,
    RB
    10,617 10,617 5,018 ? ? ? ? ? 0.064% real
    unsym.
    ? JGD_G5/
    IG5-15
    1974 MAT,
    MM,
    RB
    11,369 11,987 6,146 ? ? ? ? ? 0.24% integer
    rect.
    ? Pajek/
    Reuters911
    1517 MAT,
    MM,
    RB
    13,332 13,332 10,685 ? ? ? ? ? 0.17% integer
    sym.
    ? Pajek/
    foldoc
    1473 MAT,
    MM,
    RB
    13,356 13,356 13,239 ? ? ? ? ? 0.067% integer
    unsym.
    ? JGD_Margulies/
    kneser_8_3_1
    2165 MAT,
    MM,
    RB
    15,737 15,681 14,897 ? ? ? ? ? 0.019% binary
    rect.
    ? JGD_G5/
    IG5-16
    1975 MAT,
    MM,
    RB
    18,846 18,485 9,519 ? ? ? ? ? 0.17% integer
    rect.
    ? NYPA/
    Maragal_6
    1889 MAT,
    MM,
    RB
    21,255 10,152 10,052 ? ? ? ? ? 0.25% real
    rect.
    ? Pajek/
    EAT_RS
    1461 MAT,
    MM,
    RB
    23,219 23,219 8,210 ? ? ? ? ? 0.06% integer
    unsym.
    ? Pajek/
    EAT_SR
    1462 MAT,
    MM,
    RB
    23,219 23,219 8,210 ? ? ? ? ? 0.06% integer
    unsym.
    ? GHS_indef/
    dtoc
    1234 MAT,
    MM,
    RB
    24,993 24,993 19,994 ? ? ? ? ? 0.011% real
    sym.
    ? Boeing/
    bcsstm37
    347 MAT,
    MM,
    RB
    25,503 25,503 14,005 ? ? ? ? ? 0.0024% real
    sym.
    ? Pajek/
    HEP-th
    1502 MAT,
    MM,
    RB
    27,240 27,240 21,319 ? ? ? ? ? 0.046% binary
    unsym.
    ? Pajek/
    HEP-th-new
    1503 MAT,
    MM,
    RB
    27,770 27,770 21,776 ? ? ? ? ? 0.046% binary
    unsym.
    ? Meszaros/
    nemswrld
    1738 MAT,
    MM,
    RB
    7,138 28,550 6,647 ? ? ? ? ? 0.094% real
    rect.
    ? GHS_indef/
    bloweybl
    1424 MAT,
    MM,
    RB
    30,003 30,003 30,002 ? ? ? ? ? 0.012% real
    sym.
    ? JGD_G5/
    IG5-17
    1976 MAT,
    MM,
    RB
    30,162 27,944 14,060 ? ? ? ? ? 0.12% integer
    rect.
    ? Meszaros/
    baxter
    1692 MAT,
    MM,
    RB
    27,441 30,733 24,386 ? ? ? ? ? 0.013% real
    rect.
    ? Meszaros/
    nsct
    1819 MAT,
    MM,
    RB
    23,003 37,563 23,002 ? ? ? ? ? 0.081% integer
    rect.
    ? Meszaros/
    dbir1
    1705 MAT,
    MM,
    RB
    18,804 45,775 18,802 ? ? ? ? ? 0.13% integer
    rect.
    ? Meszaros/
    dbir2
    1706 MAT,
    MM,
    RB
    18,906 45,877 18,904 ? ? ? ? ? 0.13% integer
    rect.
    ? NYPA/
    Maragal_7
    1890 MAT,
    MM,
    RB
    46,845 26,564 25,866 ? ? ? ? ? 0.096% real
    rect.
    ? JGD_GL7d/
    GL7d13
    1986 MAT,
    MM,
    RB
    47,271 8,899 8,897 ? ? ? ? ? 0.085% integer
    rect.
    ? JGD_G5/
    IG5-18
    1977 MAT,
    MM,
    RB
    47,894 41,550 20,818 ? ? ? ? ? 0.09% integer
    rect.
    ? LPnetlib/
    lp_cre_d
    612 MAT,
    MM,
    RB
    8,926 73,948 6,476 ? ? ? ? ? 0.037% real
    rect.
    ? NYPA/
    Maragal_8
    2217 MAT,
    MM,
    RB
    33,212 75,077 18,456 ? ? ? ? ? 0.052% real
    rect.
    ? LPnetlib/
    lp_cre_b
    610 MAT,
    MM,
    RB
    9,648 77,137 7,240 ? ? ? ? ? 0.035% real
    rect.
    ? Pajek/
    Wordnet3
    1531 MAT,
    MM,
    RB
    82,670 82,670 25,994 ? ? ? ? ? 0.0019% integer
    unsym.
    ? LPnetlib/
    lp_pds_20
    652 MAT,
    MM,
    RB
    33,874 108,175 33,798 ? ? ? ? ? 0.0063% integer
    rect.
    ? Mittelmann/
    fome20
    1668 MAT,
    MM,
    RB
    33,874 108,175 33,798 ? ? ? ? ? 0.0063% integer
    rect.
    ? Bydder/
    mri1
    1317 MAT,
    MM,
    RB
    65,536 147,456 64,517 ? ? ? ? ? 0.0061% real
    rect.
    ? Bydder/
    mri2
    1318 MAT,
    MM,
    RB
    63,240 147,456 48,321 ? ? ? ? ? 0.0061% real
    rect.
    ? Mittelmann/
    pds-30
    1646 MAT,
    MM,
    RB
    49,944 158,489 49,788 ? ? ? ? ? 0.0043% integer
    rect.
    ? JGD_GL7d/
    GL7d14
    1987 MAT,
    MM,
    RB
    171,375 47,271 47,266 ? ? ? ? ? 0.023% integer
    rect.
    ? Mittelmann/
    fome21
    1669 MAT,
    MM,
    RB
    67,748 216,350 67,596 ? ? ? ? ? 0.0032% integer
    rect.
    ? Mittelmann/
    pds-40
    1647 MAT,
    MM,
    RB
    66,844 217,531 66,641 ? ? ? ? ? 0.0032% integer
    rect.
    ? Pajek/
    patents_main
    1513 MAT,
    MM,
    RB
    240,547 240,547 137,521 ? ? ? ? ? 0.00097% real
    unsym.
    ? Mittelmann/
    pds-50
    1648 MAT,
    MM,
    RB
    83,060 275,814 82,837 ? ? ? ? ? 0.0026% integer
    rect.
    ? Kamvar/
    Stanford
    979 MAT,
    MM,
    RB
    281,903 281,903 192,557 ? ? ? ? ? 0.0029% binary
    unsym.
    ? Barabasi/
    NotreDame_www
    1510 MAT,
    MM,
    RB
    325,729 325,729 102,992 ? ? ? ? ? 0.00088% binary
    unsym.
    ? Springer/
    ESOC
    1860 MAT,
    MM,
    RB
    327,062 37,830 37,349 ? ? ? ? ? 0.049% real
    rect.
    ? Mittelmann/
    pds-60
    1649 MAT,
    MM,
    RB
    99,431 336,421 99,204 ? ? ? ? ? 0.0022% integer
    rect.
    ? JGD_Relat/
    rel8
    2177 MAT,
    MM,
    RB
    345,688 12,347 12,345 ? ? ? ? ? 0.019% integer
    rect.
    ? JGD_Relat/
    relat8
    2185 MAT,
    MM,
    RB
    345,688 12,347 12,345 ? ? ? ? ? 0.031% integer
    rect.
    ? JGD_Margulies/
    kneser_10_4_1
    2163 MAT,
    MM,
    RB
    349,651 330,751 323,401 ? ? ? ? ? 0.00086% binary
    rect.
    ? Mittelmann/
    pds-70
    1650 MAT,
    MM,
    RB
    114,944 390,005 114,717 ? ? ? ? ? 0.0019% integer
    rect.
    ? Barabasi/
    NotreDame_actors
    1509 MAT,
    MM,
    RB
    392,400 127,823 114,762 ? ? ? ? ? 0.0029% binary
    rect.
    ? Buss/
    connectus
    2247 MAT,
    MM,
    RB
    512 394,792 458 ? ? ? ? ? 0.56% binary
    rect.
    ? Mittelmann/
    pds-80
    1651 MAT,
    MM,
    RB
    129,181 434,580 128,954 ? ? ? ? ? 0.0017% integer
    rect.
    ? JGD_GL7d/
    GL7d15
    1988 MAT,
    MM,
    RB
    460,261 171,375 171,373 ? ? ? ? ? 0.0077% integer
    rect.
    ? Mittelmann/
    pds-90
    1652 MAT,
    MM,
    RB
    142,823 475,448 142,596 ? ? ? ? ? 0.0015% integer
    rect.
    ? Mittelmann/
    pds-100
    1653 MAT,
    MM,
    RB
    156,243 514,577 156,016 ? ? ? ? ? 0.0014% integer
    rect.
    ? Kamvar/
    Stanford_Berkeley
    980 MAT,
    MM,
    RB
    683,446 683,446 424,014 ? ? ? ? ? 0.0016% binary
    unsym.
    ? Pajek/
    IMDB
    1504 MAT,
    MM,
    RB
    428,440 896,308 250,516 ? ? ? ? ? 0.00098% binary
    rect.
    ? JGD_Margulies/
    wheel_601
    2169 MAT,
    MM,
    RB
    902,103 723,605 723,005 ? ? ? ? ? 0.00033% binary
    rect.
    ? JGD_GL7d/
    GL7d16
    1989 MAT,
    MM,
    RB
    955,128 460,261 460,091 ? ? ? ? ? 0.0033% integer
    rect.
    ? Mittelmann/
    stormG2_1000
    1660 MAT,
    MM,
    RB
    528,185 1,377,306 526,185 ? ? ? ? ? 0.00048% real
    rect.
    ? JGD_GL7d/
    GL7d21
    1994 MAT,
    MM,
    RB
    822,922 1,437,547 822,921 ? ? ? ? ? 0.0015% integer
    rect.
    ? JGD_GL7d/
    GL7d17
    1990 MAT,
    MM,
    RB
    1,548,650 955,128 954,861 ? ? ? ? ? 0.0018% integer
    rect.
    ? Gleich/
    wikipedia-20051105
    1843 MAT,
    MM,
    RB
    1,634,989 1,634,989 927,611 ? ? ? ? ? 0.00074% binary
    unsym.
    ? JGD_GL7d/
    GL7d20
    1993 MAT,
    MM,
    RB
    1,437,547 1,911,130 1,437,546 ? ? ? ? ? 0.0011% integer
    rect.
    ? JGD_GL7d/
    GL7d18
    1991 MAT,
    MM,
    RB
    1,955,309 1,548,650 1,548,499 ? ? ? ? ? 0.0012% integer
    rect.
    ? Gleich/
    wikipedia-20060925
    1844 MAT,
    MM,
    RB
    2,983,494 2,983,494 1,676,625 ? ? ? ? ? 0.00042% binary
    unsym.
    ? Gleich/
    wikipedia-20061104
    1845 MAT,
    MM,
    RB
    3,148,440 3,148,440 1,765,239 ? ? ? ? ? 0.0004% binary
    unsym.
    ? Gleich/
    wikipedia-20070206
    1846 MAT,
    MM,
    RB
    3,566,907 3,566,907 1,992,408 ? ? ? ? ? 0.00035% binary
    unsym.
    ? Pajek/
    patents
    1514 MAT,
    MM,
    RB
    3,774,768 3,774,768 2,011,083 ? ? ? ? ? 0.00011% binary
    unsym.
    ? Gleich/
    wb-edu
    1842 MAT,
    MM,
    RB
    9,845,725 9,845,725 5,000,334 ? ? ? ? ? 5.9e-005% binary
    unsym.
    ? JGD_Relat/
    rel9
    2178 MAT,
    MM,
    RB
    9,888,048 274,669 274,667 ? ? ? ? ? 0.00087% integer
    rect.
    ? JGD_Relat/
    relat9
    2186 MAT,
    MM,
    RB
    12,360,060 549,336 274,667 ? ? ? ? ? 0.00057% integer
    rect.

    Maintained by Leslie Foster, last updated 16-Feb-2009.
    See UFget to download the above matrices directly into MATLAB.

    For use with UFget a list of Univesity of Florida matrix id's for the above matrices follows:
    1472 1974 1517 1473 2165 1975 1889 1461 1462 1234 347 1502 1503 1738 1424 1976 1692 1819 1705 1706 1890 1986 1977 612 2217 610 1531 652 1668 1317 1318 1646 1987 1669 1647 1513 1648 979 1510 1860 1649 2177 2185 2163 1650 1509 2247 1651 1988 1652 1653 980 1504 2169 1989 1660 1994 1990 1843 1993 1991 1844 1845 1846 1514 1842 2178 2186