Re: Should I cut these down?
Well, any kind of fertilizer is probably better than none. In general, for bananas you want something with a ratio of NPK (nitrogen, phosphorous, potassium) that is medium-low-high (i.e., the highest value should be for potassium). Personally, I use organic fertilizers only because they release nutrients more evenly than a massive pulse that many inorganics give you. If you soil is like most in So Cal, it is probably on the alkaline side, so using a fert. that is somewhat acidic would be good, too.
Thinning the mat is removing some stems from the clump of banana plants. A "mat" is a group of pseudostems ("trunks") that share a rhizome (corm). When there are many trunks on a single mat, they end up competing for light, nutrients, and water, which can decrease the size of the bananas and the number of bananas in each bunch.
If your soil is clay like mine, then 10 minutes of watering a day is probably enough.
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