This paper discusses quasi-orthogonal matrices which were first highlighted by J. J. Sylvester and J. Hadamard, who showed that two level matrices exist for even orders 4t, t integer. We consider two-level matrices complementing the Hadamard, Mersenne and Euler matrices. We give definitions of golden ratio matrices as illustrations for some elementary and interesting cases, and reveal some new properties. The definitions of a section and a layer of quasi-orthogonal matrices are provided. The

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... mple of continuous matrices with varying levels is used to show, that the golden section matrices branch is closely associated with Hadamard and conference matrices. Commentaries on the applied aspects of the golden section matrices use are provided here as well. Mathematics Subject Classification: 05B20; 20B20