{"@context":"http://iiif.io/api/presentation/2/context.json","@type":"sc:Manifest","@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/manifest","label":"The Rank of Recurrence Matrices","metadata":[{"label":"Title","value":"The Rank of Recurrence Matrices"},{"label":"Collection","value":["Mathematics Faculty Publications"]},{"label":"Relation","value":"mth"},{"label":"Author","value":"Christopher Lee, Valerie Peterson"},{"label":"Journal Title","value":"The College Mathematics Journal"},{"label":"Abstract","value":"A recurrence matrix is defined as a matrix whose entries (read left-to-right, row-by-row) are sequential elements generated by a linear recurrence relation. The maximal rank of this matrix is determined by the order of the corresponding recurrence. In the case of an order-two recurrence, the associated matrix fails to have full rank whenever the ratio of the two initial values of the sequence is an eigenvalue of the relation."},{"label":"DOI","value":"10.4169/college.math.j.45.3.207"},{"label":"Volume","value":"45"},{"label":"Issue","value":"3"},{"label":"Publication Date","value":"D:00 M:05 Y:2014"},{"label":"Publication Information","value":"The College Mathematics Journal, 2014, Volume 45, Issue 3, 207-215. © 2014 Mathematical Association of America Archived version is the final published version."}],"description":"The Rank of Recurrence Matrices","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_1","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-02","height":1651,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/443d82ca-19c3-4cf4-bffc-597b5cec3416/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/443d82ca-19c3-4cf4-bffc-597b5cec3416","profile":"http://iiif.io/api/image/2/level2.json","tiles":[{"width":512,"scaleFactors":[1,2,4]}]},"height":1651,"width":1275},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_1","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/443d82ca-19c3-4cf4-bffc-597b5cec3416/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_2","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-03","height":1651,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/51d22fce-820d-4fd5-99d3-f2ab3c13d5d1/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/51d22fce-820d-4fd5-99d3-f2ab3c13d5d1","profile":"http://iiif.io/api/image/2/level2.json","tiles":[{"width":512,"scaleFactors":[1,2,4]}]},"height":1651,"width":1275},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_2","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/51d22fce-820d-4fd5-99d3-f2ab3c13d5d1/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_3","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-04","height":1651,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/aefe6474-4811-4118-9ae1-42a9bfc09997/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/aefe6474-4811-4118-9ae1-42a9bfc09997","profile":"http://iiif.io/api/image/2/level2.json","tiles":[{"width":512,"scaleFactors":[1,2,4]}]},"height":1651,"width":1275},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_3","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/aefe6474-4811-4118-9ae1-42a9bfc09997/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_4","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-05","height":1653,"width":1278,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/621c13cc-64ce-4a50-aa01-be6ca9473f69/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/621c13cc-64ce-4a50-aa01-be6ca9473f69","profile":"http://iiif.io/api/image/2/level2.json","tiles":[{"width":512,"scaleFactors":[1,2,4]}]},"height":1653,"width":1278},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_4","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/621c13cc-64ce-4a50-aa01-be6ca9473f69/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_5","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-06","height":1653,"width":1278,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/bfa26684-0c27-44ec-a27b-a56f2c27bfe3/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/bfa26684-0c27-44ec-a27b-a56f2c27bfe3","profile":"http://iiif.io/api/image/2/level2.json","tiles":[{"width":512,"scaleFactors":[1,2,4]}]},"height":1653,"width":1278},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_5","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/bfa26684-0c27-44ec-a27b-a56f2c27bfe3/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_6","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-07","height":1651,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/5e94496e-5e8f-44bc-8c73-e7a32a5e5e61/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/5e94496e-5e8f-44bc-8c73-e7a32a5e5e61","profile":"http://iiif.io/api/image/2/level2.json","tiles":[{"width":512,"scaleFactors":[1,2,4]}]},"height":1651,"width":1275},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_6","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/5e94496e-5e8f-44bc-8c73-e7a32a5e5e61/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_7","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-08","height":1651,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/e562768d-37ff-4dc6-9d23-ef387f38a3e3/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/e562768d-37ff-4dc6-9d23-ef387f38a3e3","profile":"http://iiif.io/api/image/2/level2.json"},"height":1651,"width":1275},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_7","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/e562768d-37ff-4dc6-9d23-ef387f38a3e3/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_8","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-09","height":1651,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/cfddd76e-fd9a-4463-978e-4ae52482d0e4/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/cfddd76e-fd9a-4463-978e-4ae52482d0e4","profile":"http://iiif.io/api/image/2/level2.json"},"height":1651,"width":1275},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_8","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/cfddd76e-fd9a-4463-978e-4ae52482d0e4/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}},{"@id":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_9","@type":"sc:Canvas","label":"The Rank of Recurrence Matrices-10","height":1651,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://iiif.quartexcollections.com/portland/iiif/0939a260-16d9-42af-a760-cbbc524108a3/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://iiif.quartexcollections.com/portland/iiif/0939a260-16d9-42af-a760-cbbc524108a3","profile":"http://iiif.io/api/image/2/level2.json"},"height":1651,"width":1275},"on":"https://iiif.quartexcollections.com/portland/iiif/c1ce827c-d41b-4db9-8a3a-d3167941070e/canvas/_9","metadata":[]}],"thumbnail":{"@id":"https://iiif.quartexcollections.com/portland/iiif/0939a260-16d9-42af-a760-cbbc524108a3/full/500,500/0/default.jpg","@type":"dctypes:Image","height":500,"width":500}}]}],"thumbnail":"https://iiif.quartexcollections.com/portland/iiif/443d82ca-19c3-4cf4-bffc-597b5cec3416/full/300,300/0/default.jpg","logo":"https://iiif.quartexcollections.com/portland/iiif/logo"}