PLACING ZEROES and the KRONECKER CANONICAL FORM Www Users Cs Umn

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[Music] foreign so we've been talking a lot about how to solve systems of differential equations Matrix Systems of first order differential equations x dot equals ax where a is a matrix and X is a vector of states and I essentially you know have X as an n-dimensional Vector with n components a is an N by n Matrix and this would represent n first order ordinary differential equations A first order differential equation for X1 for X2 for X3 and so on and so forth down to xn and we've looked at looked at simple cases where a has distinct eigenvalues eigenvalues that are not repeated and so today I'm going to talk about what happens when you have repeated eigenvalues so specifically I'm actually going to look at two cases two different a matrices that have repeated eigenvalues the first one I'm going to look at is the case a equals 1 0 0 1 which is almost trivially easy because it's already diagonal but again this does have two distinct sorry two repeated eigenvalues Lambda equals one and