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