Factor Analysis Development

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Presentation transcript:

Factor Analysis Development This presentation is partially animated. Only use the control panel at the bottom of screen to review what you have seen. When using your mouse, make sure you click only when it is within the light blue frame that surrounds each slide.

[ ] [ ] l l D Z Z Z Z Q -1 Z Q Z Q Q Q j Q n Z = D # A + B T j Factor Analysis Development Z = D # T A + B always a diagonal matrix Sometimes the identity matrix A is (The complete story in two slide) D Z CO Z CM Z RO Z RM Find Q such that [ ] Q -1 A diagonal matrix Z Q If you are successful then = Each of these is an eigenvalue l [ ] l j Z Q Q Q j = Each of these is an eigenvector Each of these columns (eigenvectors) is linearly independent Q n will make a great orthonormal basis set orthogonal

( ) ( ) D = RC Z Q n Q n Q n D D U Q n D U D I Q n D Q n Q n Q n Q n D Factor Analysis Development D = RC (The complete story in two slide) Z Q n -1 T Q n -1 Q n ( ) D T D = U Q n D U D = I T Q n D T -1 Q n -1 Q n -1 Q n -1 Q n D T U D Q n = ( ) U T Q n D T U D Q n = U U T U

( ) D = RC Z Q D n I U -1 T = Factor Analysis Development (The complete story in two slide)