Grenzmatrix stationäre Matrix M0704

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Überlässt man eine Population für lange Zeit sich selbst, pendelt sich meist eine „Endverteilung“ ein. Diese langfristige Entwicklung einer Population wird durch die „Grenzmatrix“ oder „stationäre Matrix“ beschrieben. Die Grenzmatrix zeichnet sich dadurch aus, dass sie aus lauter gleichen Spalten besteht. Es gibt zwei Arten sie zu berechnen: Möglichkeit 1. Mit GTR/CAS: Hat man einen Taschenrechner oder Computerprogramm, welches Matrizenmultiplikation beherrscht, tippt man einfach mal: Matrix hoch 100 oder Matrix hoch 500 oder... Enthält das Ergebnis lauter gleiche Spalten, so ist das eigentlich schon die Grenzmatrix. Möglichkeit 2. Rechnen von Hand: Man braucht leider den stationären Vektor dazu. Die Grenzmatrix enthält lauter Unbekannte (allerdings in jeder Spalte die gleichen). Nun führt man eine Matrizenmultiplikation mit dem stationären Vektor durch und da das Ergebnis wieder der statinoäre Vektor ist erhält man nach wenigen Schritten drei, vier sehr einfache Gleichungen auf Kindergarten-Niveau. 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