Helligkorsgade, Kølding, DK (built 1589; photo from WikimediaCommons by User:Mahlum, 2006)
Danish Demes
a Regional DNA Project for Danish Americans and Danes around the World
Borches gård, Kolding, DK (built 1595; photo from WikimediaCommons by User:Mahlum, 2006)
Carsten Andersen MATTHIESEN, Jr.
Maria M. KONSTMAN
Husband:  Carsten Andersen MATHIESEN / MATTHIESEN
Birth:  6 Feb 1881, Weisby, Schleswig-Holstein, DEU / Visby, Visby Sogn, TH&L Herred, Tønder Amt, DK
Death:  20 Jan 1947, Placer Co., CA
Transhumance:  6-18 May 1903, Copenhagen to Ellis Island, NY, on the ship Hellig Olav
Event:  1908, naturalized U.S. citizen
Occupation:  moulder, riveter
Father:  Carsten Andersen MATHIESEN, Sr.
Mother:  Marie Magdalen FRIEDRICHSEN
Marriage:  1909
Residence in 1910:  Oakland, Alameda Co., CA
Residence in 1920:  Vallejo, Solano Co., CA
Residence in 1930:  Sacramento, Sacramento Co., CA
Wife:  Maria M. KONSTMAN [KUNZMAN?]
Birth:  19 Apr 1884, DEU
Death:  20 Apr 1951, Placer Co., CA
Transhumance:  1905, to America
Event:  1908, naturalized U.S. citizen
Occupation:  homemaker
Children:
1.  Charles A. MATTHIESEN, b. 8 Jul 1910, CA; d. 17 Jun 1971, Orange Co., CA
Keywords for search engines:  genealogy;    FRG, Germany, Deutschland; Denmark, Danmark; TH&L = Tønder, Højer og Lø; USA, United States, California, New York

Sources:

1.  Mathiesen Pedigree by Søren H. Schmidt, Lokalhistorisk Arkiv, Bredebro, DK.

2a.  The Danish Emigration Archives, Aalborg, Denmark (online at www.emiarch.dk):
Name: Mathiesen, Carsten Andersen
Age: 22
Occupation: Landarbejder*
Birth Place: Slesvig
Last Residence City/Parish/County: Slesvig, ?, Slesvig
Destination City/State/Country: New York City, New York State, USA
Registraton Date: 5/6/1903
Name of Ship: Hellig Olav
Contract No. / IDCode: 180400 / D0103M2911
*farm laborer (one who does not own the land they work, as opposed to a farmer, who does)

2b.  Ellis Island Immigration Records:  Passenger Record (online at www.ellisislandrecords.org):
PASSENGER RECORD
Name: Mathiesen, Carsten A.
Ethnicity: Germany, Scandinavian
Place of Residence: Germany
Date of Arrival: May 18, 1903
Age on Arrival: 22y 2m
Gender: M
Marital Status: S
Ship of Travel: Hillig Olav
Port of Departure: Copenhagen City, Copenhagen, Denmark
Couldn't find Maria, but I may not have searched exhaustively enough — or she may not have come through Ellis Island.

3.  Marriage Record:

4.  1910 Census Index/Images (online at Genealogy.com; Image #13 of 432):  243 Hannah Street, Oakland City (Ward 2), Oakland Twp., Alameda Co., CA, Roll 70 (Book 1), p. 7A, SN 7A, SD 3, ED 87, enumerated 21 Apr 1910, official enumeration date 15 Apr 1910 (extracted by Diana Gale Matthiesen):
1910:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 26 29 30 31 32
* 243 140 150 Matthiesen Carsten Head M W 29 M1 0 0 0 Ger-Danish Ger-Danish Ger-Danish 1903 Na Eng Farmer Moulder Foundry W N Y Y R 15 8 9 X
      __________ Maria Wife F W 26 M1 0 0 0 Ger-Danish Ger-Danish Ger-Danish 1905   Eng None         Y Y          
*Hannah Street

5.  1920 Census Index/Images (online at Ancestry.com; Image #26 of 59):  1925 Marin St., [Vallejo City,] Vallejo Twp., Solano Co., VA, p. 49B, SN 13B, SD 3, ED 207, enumerated 15 Jan 1920, official enumeration date 1 Jan 1920 (extracted by Diana Gale Matthiesen).
1920:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
* 1925 224 281 Matthiesen Carsten Head R M W 38 M 1903 na 1908   Y Y Ger Dan Ger Dan Ger Dan Y Riviter Navy Yard W
      __________ Maria Wife     W 35 M 1905 na 1908   Y Y Ger Dan Ger Dan Ger Dan Y none    
      __________ Charles A? Son     W 9 S       Y     CA   Ger Dan Ger Dan   none    
      __________ Peter Bro     W 44 D 1893 na 1899   Y Y Ger Dan Ger Dan Ger Dan Y Riviter Navy Yard W
* Marin Street
Carsten's and Peter's brother, Mathies MATTHIESEN, is three pages away, also a riveter in the naval yard. 

6.  1930 Census Index/Images (online at Ancestry.com; Image #11 of 14):  Mariposa Ave., Center Twp., Sacramento Co., CA, p. 19B, SN 6B, ED 34-15, SD 3, enumerated 11 Apr 1930, official enumeration date 1 Apr 1930 (extracted by Diana Gale Matthiesen):
1920:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
1 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32
* 154 157 Matthiesen Ceisten Head O R Y M W 49 M 29 N Y DK DK DK Danish 1901 Na Y Riveter Car Shops W Y N 113
    __________ Marria Wife       F W 45 M 25 N Y DK DK DK Danish 1905 Na Y None          
    __________ Charles Son       M W 19 S   N Y CA DK DK       Y Clerk Cigar Store W Y    
*Mariposa Ave

7.  California Death Index (online at RootsWeb.com; missing columns contained no data):
Last
Name
First
Name
Middle Birth
Date
Mother
Maiden
Father
Last
Sex Birth
Place
Death Place
(County)
Death
Date
SSN Age
Matthiesen Carsten A 02/06/1881 Fredricksen Matthiesen M Rest (Other) Placer 01/20/1947 700-09-0159 65 yrs
Matthiesen Maria M 04/19/1884   Konstman F Rest (Other) Placer 04/20/1951   67 yrs
Matthiesen Charles A 07/08/1910     M California Orange 06/17/1971 557-22-4402 60 yrs
There appears to be no such surname as KONSTMAN.  Maria's surname is most likely KUNZMAN — at least, that's the closest surname I could find, and even it is rare.

8.  World War I Selective Service System Draft Registration Cards, 1917-18.  Microfilm Series M1509 (4277 rolls), National Archives and Records Administration, Washington, DC (card images and index online at Ancestry.com):
Roll | Serial No. | Order No: 1530652 | 2209 | A1033
Name: Carson Anderson Matthiesen
Permanent Home Address: 1813 9th St. Alameda Alameda California
Age in Years | Date of Birth: 37 | Feby 6th 1881
Race: White
U.S. Citizen: Naturalized
Present Occupation: Riverter
Employer's Name: Hanlon Dry Dock & [??] Co
Place of Employment: Foot [?? ??] Oakland Cal
Nearest Relative: Name: Maty Matthiesen Wife
Nearest Relative: Address: 1813 9th St. Alameda Cal
Signature: C A Matthiesen
Height (tall, medium, short): Tall
Build (slender, medium, stout): Medium
Color of Eyes | Color of Hair: Blue | Light
Physically Disabled:  
Date of Registration: 9 12 '18
Draft Board: #1 City of Alameda

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Memorial stone for King Erik I (c1060-1103), a.k.a., 'Erik the Good' or Erik Ejegod; Borgvold, Viborg Amt, DK (photo from WikimediaCommons by User:Calvin, 2007). Viking burial ground (700-1150 CE), Lindholm Høje, Aalborg Amt, DK (photo from WikimediaCommons by User:Bunnyfrosch, 2007).

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