In this bachelor thesis we formulate the algorithm for finding eigenvalues and eigenvectors without the use of determinant. For the algorithm to work, the understanding of linear independance and dependance is crucial, that is why we chose to present these two principles in more detail. We defined eigenvalues, eigenvectors, matrix polynomial, minimal polynomial of the matrix, and minimal polynomial of a vector with respect to matrix. These definitions and theorems helped us to construct our algorithm. We built our method step-by-step through our bachelor thesis. First, we used it on non defective matrices. Then we defined defective matrices, generalized vectors and Jordan chain of generalized eigenvectors. Throughout the thesis, examples are used to show what we have discovered till then. In the end, we formulated the whole universal algorithm, which works no matter what kind of the matrix we start with.
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